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question_answer1)
Which of the following is a cubic polynomial whose zeros are (-1), (-2) and (-3)?
A)
\[{{p}^{3}}-6\] done
clear
B)
\[{{p}^{3}}-6{{p}^{2}}+6\] done
clear
C)
\[{{p}^{3}}+6{{p}^{2}}+11p+6\] done
clear
D)
\[{{p}^{3}}-6{{p}^{3}}-11p-6\] done
clear
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question_answer2)
2 and (-2) are two zeros of the polynomial\[\text{34}\,{{\text{m}}^{\text{4}}}-\text{4m}+\text{12}0\]. What are the other two zeros of the polynomial?
A)
5,-6 done
clear
B)
-5, 6 done
clear
C)
-5,-6 done
clear
D)
5, 6 done
clear
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question_answer3)
Find the value of the polynomial \[p(x)={{x}^{2}}+3x-2\]when x = (-1).
A)
-4 done
clear
B)
3 done
clear
C)
4 done
clear
D)
6 done
clear
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question_answer4)
For what value of 'm' is one zero of the polynomial\[({{m}^{2}}+9){{x}^{2}}+13x+6m\], the reciprocal of the other?
A)
9 done
clear
B)
-3 done
clear
C)
6 done
clear
D)
3 done
clear
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question_answer5)
Identify the polynomial whose sum of zeros is (-5) and their product is 6.
A)
\[{{x}^{2}}-4x-12\] done
clear
B)
\[{{x}^{2}}+4x+12\] done
clear
C)
\[{{p}^{2}}+6p-4\] done
clear
D)
\[{{x}^{2}}-5x+6\] done
clear
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question_answer6)
\[\alpha \]and\[\beta \]are the zeros of a polynomial, such that\[\alpha +\beta =6\]and\[\alpha \beta =4\]. Identify the polynomial.
A)
\[{{x}^{2}}-6x+4\] done
clear
B)
\[{{a}^{2}}+6a+4\] done
clear
C)
\[{{p}^{2}}+6p-4\] done
clear
D)
\[{{m}^{2}}-6m-4\] done
clear
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question_answer7)
Identify the zeros of the polynomial\[p(t)={{t}^{3}}-3{{t}^{2}}-10t+24\]
A)
-2,-3,-4 done
clear
B)
-2, -3, 4 done
clear
C)
2,-3, 4 done
clear
D)
2, -3, -4 done
clear
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question_answer8)
What is the quotient when\[\text{2}{{\text{m}}^{\text{2}}}-\text{m}+\text{3}\]is divided by (2 - m) leaving a remainder 9?
A)
-2m + 3 done
clear
B)
-(2m - 3) done
clear
C)
2m + 3 done
clear
D)
-(2m + 3) done
clear
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question_answer9)
Choose the cubic polynomial whose zeros are-2,3 and 5.
A)
\[{{\text{p}}^{\text{3}}}-\text{6}{{\text{p}}^{\text{2}}}-\text{p}+\text{3}0\] done
clear
B)
\[{{\text{x}}^{\text{3}}}\text{+6}{{\text{x}}^{\text{2}}}-\text{x-3}0\] done
clear
C)
\[{{\text{x}}^{\text{3}}}-\text{6}{{\text{x}}^{\text{2}}}+\text{x}-\text{3}0\] done
clear
D)
\[{{\text{p}}^{\text{3}}}+\text{6}{{\text{p}}^{\text{2}}}+\text{p}-\text{3}0\] done
clear
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question_answer10)
Choose the zeros of the polynomial\[6{{x}^{2}}-7x-3\]
A)
\[\frac{1}{3},\frac{-1}{2}\] done
clear
B)
\[\frac{-1}{3},\frac{3}{2}\] done
clear
C)
\[\frac{-1}{3},\frac{-1}{2}\] done
clear
D)
\[\frac{1}{3},\frac{1}{2}\] done
clear
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question_answer11)
Which of the following is the division algorithm of polynomials if dividend = f(x), divisor = p(x), quotient = q(x) and remainder = r(x)?
A)
f(x) = r(x) p(x) + q(x) done
clear
B)
f(x) = p(x) q(x) + r(x) done
clear
C)
f(x) = p(x) q(x) - r(x) done
clear
D)
f(x) = p(x) r(x) - q(x) done
clear
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question_answer12)
a, p and y are the zeros of a cubic polynomial. If \[\alpha +\beta +\gamma =2\],\[\alpha \beta +\beta \gamma +\gamma \alpha =(-7)\]and\[\alpha \beta \gamma =(-14)\] find the polynomial.
A)
\[{{x}^{3}}-2{{x}^{2}}-7x+14\] done
clear
B)
\[{{m}^{3}}+2{{m}^{2}}-7m-14\] done
clear
C)
\[{{n}^{3}}-2{{n}^{2}}+7n-14\] done
clear
D)
\[{{y}^{3}}+2{{y}^{2}}-7y-14\] done
clear
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question_answer13)
Find the remainder when\[\text{5}{{\text{p}}^{\text{3}}}-\text{13}{{\text{p}}^{\text{2}}}+\text{21p}-14\]is divided by\[(\text{3}-\text{2p}+{{\text{p}}^{\text{2}}})\].
A)
-5 done
clear
B)
-15 done
clear
C)
-10 done
clear
D)
5 done
clear
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question_answer14)
The polynomial \[{{\text{a}}^{\text{3}}}-\text{3}{{\text{a}}^{\text{2}}}+\text{a}+\text{2}\]is divided by a polynomial g[a].The quotient and remainder obtained are (a - 2) and (-2a + 4) respectively. Find g[a].
A)
\[{{\text{a}}^{\text{2}}}+\text{a}+\text{1}\] done
clear
B)
\[{{\text{a}}^{\text{2}}}-\text{a}+\text{1}\] done
clear
C)
\[{{\text{a}}^{\text{2}}}-\text{a}-\text{1}\] done
clear
D)
\[{{\text{a}}^{\text{2}}}+\text{a}-\text{1}\] done
clear
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question_answer15)
Choose the zeros of the polynomial whose graph is given.
A)
1.-1.2 done
clear
B)
-2, 1, 3 done
clear
C)
-2, 0, 3 done
clear
D)
-2, 2, 3 done
clear
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question_answer16)
What is the nature of the zeros of the quadratic polynomial\[{{x}^{2}}+\text{88}x+\text{125}\]?
A)
Both positive done
clear
B)
Both negative done
clear
C)
One positive, one negative done
clear
D)
Cannot be said done
clear
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question_answer17)
If\[\alpha \]and\[\beta \]are the zeros of\[p(x)=2{{x}^{2}}-6+6x\], which of the following is correct?
A)
\[\alpha +\beta <\alpha \beta \] done
clear
B)
\[\alpha +\beta >\alpha \beta \] done
clear
C)
\[\alpha +\beta >\alpha \beta \] done
clear
D)
\[\alpha +\beta =\alpha \beta \] done
clear
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question_answer18)
If a polynomial p(x) is divided by another polynomial g(x),with a quotient q(x) and remainder r(x),then p(x) = q(x) g(x)+ r(x). What is the condition that r(x) must satisfy?
A)
r(x) = 0 done
clear
B)
r(x) = 0 or deg of r(x) > deg g(x) always. done
clear
C)
Either r(x) = 0 or deg (g(x)) > deg r(x) done
clear
D)
r(x) = g(x) done
clear
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question_answer19)
If P and Q are the zeros of the polynomial \[a{{x}^{2}}+bx+c\], what is the value of \[{{\text{P}}^{\text{2}}}+{{\text{Q}}^{\text{2}}}\]?
A)
\[\frac{{{b}^{2}}+2ac}{{{a}^{2}}}\] done
clear
B)
\[\frac{{{a}^{2}}+2bc}{{{b}^{2}}}\] done
clear
C)
\[\frac{{{a}^{2}}-2bc}{{{b}^{2}}}\] done
clear
D)
\[\frac{{{b}^{2}}-2ac}{{{a}^{2}}}\] done
clear
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question_answer20)
The zeros of the polynomial \[{{\text{n}}^{\text{3}}}+\text{9}\,{{\text{n}}^{\text{2}}}+23\,n\]\[+15\]are a - d, a and a + d. What is the value of 'a'?
A)
4 done
clear
B)
-3 done
clear
C)
6 done
clear
D)
3 done
clear
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question_answer21)
Find the zeros of the polynomial\[4{{n}^{2}}+5\sqrt{2}n-3\]
A)
\[\frac{-3\sqrt{2}}{2},\frac{\sqrt{2}}{4}\] done
clear
B)
\[3\sqrt{2},\sqrt{2}\] done
clear
C)
\[\frac{3\sqrt{2}}{4},\frac{\sqrt{2}}{4}\] done
clear
D)
\[-3\sqrt{2},\sqrt{2}\] done
clear
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question_answer22)
Which of the following is the graph of a linear polynomial?
A)
B)
C)
D)
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question_answer23)
Choose the graph of a quadratic polynomial.
A)
B)
C)
D)
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question_answer24)
If one zero of the quadratic polynomial \[2{{x}^{2}}-(3k+1)x-9\]is negative of the other, find the value of 'k'.
A)
\[-\frac{1}{6}\] done
clear
B)
3 done
clear
C)
\[\frac{1}{4}\] done
clear
D)
\[-\frac{1}{3}\] done
clear
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question_answer25)
Identify the quadratic polynomial with no zeros.
A)
B)
C)
D)
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question_answer26)
The graphs of y= f(x) are given in figures. For which of these is f(x) neither linear nor quadratic?
A)
B)
C)
D)
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question_answer27)
A cubic polynomial \[a{{x}^{3}}+b{{x}^{2}}+cx+d\] with real coefficients has at the most 'n' real zeros. Find the value of 'n'.
A)
2 done
clear
B)
1 done
clear
C)
3 done
clear
D)
4 done
clear
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question_answer28)
Find the sum of zeros of the polynomial \[2{{x}^{2}}-9\].
A)
0 done
clear
B)
1 done
clear
C)
-1 done
clear
D)
2 done
clear
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question_answer29)
If a and p are two zeros of the quadratic polynomial \[p(x)=2{{x}^{2}}-3x+7\], find the value of \[{{\text{a}}^{\text{3}}}+{{\text{p}}^{\text{3}}}\].
A)
\[\frac{37}{2}\] done
clear
B)
\[\frac{-37}{2}\] done
clear
C)
\[\frac{-99}{8}\] done
clear
D)
\[\frac{27}{2}\] done
clear
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question_answer30)
What is the relation between the zeros and the coefficients of the polynomial \[4\sqrt{3}{{x}^{2}}+5x-2\sqrt{3}\]?
A)
\[\text{Sum of zeros }=\frac{-(\text{coefficient of x})}{(\text{coefficient of }{{\text{x}}^{\text{2}}})}\] done
clear
B)
\[\text{Sum of zeros }=\frac{(\text{coefficient of x})}{(\text{coefficient of }{{\text{x}}^{\text{2}}})}\] done
clear
C)
\[\text{Sum of zeros }=\frac{(\text{coefficient of }{{\text{x}}^{2}})}{(\text{coefficient of x})}\] done
clear
D)
\[\text{Sum of zeros }=\frac{(\text{coefficient of }{{\text{x}}^{2}})}{cons\tan t}\] done
clear
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question_answer31)
If the sum of the squares of zeros of the polynomial \[6{{x}^{2}}+x+k\]is \[\frac{25}{36}\], find the value of 'k'.
A)
2 done
clear
B)
-2 done
clear
C)
24 done
clear
D)
? 24 done
clear
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question_answer32)
Choose the graph of a cubic polynomial.
A)
B)
C)
D)
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question_answer33)
Find a quadratic polynomial, whose sum and product of zeros are\[\frac{-10}{\sqrt{3}}\]and 7 respectively.
A)
\[{{x}^{2}}+\frac{10}{\sqrt{3}}x+\frac{7}{\sqrt{3}}\] done
clear
B)
\[\sqrt{3}{{x}^{2}}-10x+7\sqrt{3}\] done
clear
C)
\[\sqrt{3}{{x}^{2}}+10x+7\sqrt{3}\] done
clear
D)
\[{{x}^{2}}+10x+7\sqrt{3}\] done
clear
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question_answer34)
Find the quadratic polynomial one of whose zeros is\[\frac{\sqrt{3}}{4}\]and the product of zeros is\[\frac{1}{2}\].
A)
\[4\sqrt{3}{{x}^{2}}+5x+2\sqrt{3}\] done
clear
B)
\[{{x}^{2}}+\frac{5}{4\sqrt{3}}x-\frac{1}{2}\] done
clear
C)
\[4\sqrt{3}-5x+2\sqrt{3}\] done
clear
D)
\[2{{x}^{2}}+\frac{5}{4\sqrt{3}}x-\frac{1}{2}\] done
clear
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question_answer35)
A quadratic polynomial\[\text{f(x)}=\text{2}\times \text{2}-\text{mx}+n\]has \[\alpha \] and \[\beta \] as its two zeros. Find the value of\[~{{\alpha }^{\text{2}}}+{{\beta }^{\text{2}}}\].
A)
\[\frac{1}{8}({{m}^{2}}-4n)\] done
clear
B)
\[\frac{1}{4}({{m}^{2}}+4n)\] done
clear
C)
\[\frac{1}{4}({{m}^{2}}-4n)\] done
clear
D)
\[\frac{1}{3}({{m}^{2}}+4n)\] done
clear
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question_answer36)
The zeros of a quadratic polynomial\[f(x)=2{{x}^{2}}-mx+n\]are\[\alpha \]and\[\beta \]such that\[\alpha -\beta =3\]. Find the value of 'k'.
A)
10 done
clear
B)
2 done
clear
C)
5 done
clear
D)
15 done
clear
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question_answer37)
The zeros of the quadratic polynomial \[\text{p(x)}=\text{6}{{\text{x}}^{\text{2}}}+\text{mx}+\text{2n}\]are\[-\frac{3}{2}\]and\[\frac{4}{3}\].Find the respective values of 'm' and 'n'.
A)
2 and 3 done
clear
B)
6 and 4 done
clear
C)
3 and 5 done
clear
D)
1 and 6 done
clear
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question_answer38)
If one of the zeros of the quadratic polynomial \[\text{f(x)}=\text{3}{{\text{x}}^{\text{2}}}-\text{2}0\text{x}+\text{3p}+\text{4}\]is four times the other, find the value of 'p'.
A)
\[\frac{76}{6}\] done
clear
B)
\[\frac{52}{9}\] done
clear
C)
\[\frac{25}{4}\] done
clear
D)
\[\frac{36}{5}\] done
clear
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question_answer39)
The zeros of the quadratic polynomial\[{{x}^{2}}+4x+k\]are\[\alpha \]and\[\beta \]. Find the value of 'k' if\[\text{5}\alpha +\text{2}\beta =\text{1}\].
A)
20 done
clear
B)
? 11 done
clear
C)
-21 done
clear
D)
35 done
clear
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question_answer40)
Find\[{{\alpha }^{-1}}+{{\beta }^{-1}}\]if\[\alpha \]and\[\beta \]are the zeros of the polynomial\[\text{f(x)}=\text{9}{{\text{x}}^{\text{2}}}-\text{3x}-\text{2}\].
A)
\[\frac{-3}{2}\] done
clear
B)
\[\frac{5}{3}\] done
clear
C)
\[\frac{-2}{7}\] done
clear
D)
\[\frac{2}{7}\] done
clear
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question_answer41)
Find the cubic polynomial with the sum of its zeros, sum of the products of its zeros taken two at a time and the product of its zeros as \[\frac{1}{4},-\frac{3}{2}\] and \[\frac{9}{16}\]respectively.
A)
\[{{x}^{2}}-\frac{1}{2}{{x}^{2}}-3x+\frac{9}{16}\] done
clear
B)
\[16{{x}^{3}}-4{{x}^{2}}-24x-9\] done
clear
C)
\[{{x}^{3}}+\frac{1}{4}{{x}^{2}}-4x+16\] done
clear
D)
\[16{{x}^{3}}-5{{x}^{2}}+21x-7\] done
clear
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question_answer42)
When is a real number 'a' called the zero of the polynomial f(x) ?
A)
f(0)=a done
clear
B)
f=a done
clear
C)
f=0 done
clear
D)
f=f(0) done
clear
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question_answer43)
Which of the following is the quadratic polynomial whose zeros are\[\frac{1}{3}\]and\[\frac{-2}{5}\]?
A)
\[15{{x}^{2}}+x-2\] done
clear
B)
\[15{{x}^{2}}+5x-6\] done
clear
C)
\[15{{x}^{2}}-5x+6\] done
clear
D)
\[15{{x}^{2}}-x+2\] done
clear
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question_answer44)
If the sum of the zeros of the polynomial \[\text{f(x)}=({{\text{k}}^{\text{2}}}-\text{14}){{\text{x}}^{\text{2}}}-\text{2x}-\text{12}\]is 1, which is one of the possible values of 'k' ?
A)
\[\sqrt{14}\] done
clear
B)
-14 done
clear
C)
2 done
clear
D)
-4 done
clear
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question_answer45)
If \[\alpha \]and \[\beta \]are the zeros of the polynomial, \[f(x)={{x}^{2}}+ax-b\] find the polynomial having zeros \[\frac{1}{\alpha }\]and\[\frac{1}{\beta }\].
A)
\[ab{{x}^{2}}+bx-a\] done
clear
B)
\[{{x}^{2}}-\frac{a}{b}x-\frac{1}{b}\] done
clear
C)
\[ab{{x}^{2}}-bx+a\] done
clear
D)
\[{{x}^{2}}-\frac{b}{a}x+\frac{1}{a}\] done
clear
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question_answer46)
If the product of two of the zeros of the polynomial \[\text{p(x)}={{\text{x}}^{\text{3}}}+\text{6}{{\text{x}}^{\text{2}}}-\text{x}-\text{3}0\]i\[-\,\text{6}\], what is the third zero of p(x)?
A)
6 done
clear
B)
5 done
clear
C)
- 1 done
clear
D)
? 5 done
clear
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question_answer47)
If \[\alpha ,\beta \] and y are the zeros of the polynomial\[\text{6}{{\text{x}}^{\text{3}}}+\text{31}{{\text{x}}^{\text{2}}}-\text{29x}+\text{6}\], what is the value of\[(\alpha \beta +\beta \gamma +\gamma \alpha )\]?
A)
- 29 done
clear
B)
\[\frac{31}{6}\] done
clear
C)
\[\frac{-29}{6}\] done
clear
D)
- 1 done
clear
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question_answer48)
Which of the following is a zero of the cubic polynomial\[\text{f(x)}={{\text{x}}^{\text{3}}}-\text{3x}+\text{2}\]?
A)
- 2 done
clear
B)
- 1 done
clear
C)
0 done
clear
D)
2 done
clear
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question_answer49)
Identify polynomials from the following.
(i) \[\frac{2}{{{x}^{2}}}-3x+2\] |
(ii) \[2{{x}^{1}}+3-4x\] |
(iii) \[\frac{1}{3}{{x}^{2}}-3\] |
(iv) \[\sqrt{x}-6\] |
A)
(i) and (ii) only done
clear
B)
(ii) and (iii) only done
clear
C)
(i) and (iii) only done
clear
D)
(ii) and (iv) only done
clear
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question_answer50)
The general quadratic polynomial is\[p(x)=\]\[a{{x}^{2}}+bx+c,a\ne 0\]. If\[\alpha \]and\[\beta \]are its zeros, which of the following is true?
A)
\[\alpha +\beta =\frac{-b}{a}\] done
clear
B)
\[\alpha -\beta =\frac{b}{a}\] done
clear
C)
\[\alpha \beta =\frac{a}{c}\] done
clear
D)
\[\frac{\alpha }{\beta }=\frac{c}{a}\] done
clear
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question_answer51)
\[\alpha \],\[\beta \]and y are the zeros of the polynomial\[a{{x}^{3}}+b{{x}^{2}}+cx+d,a\ne 0\]. What is\[\alpha +\beta +\gamma \]?
A)
\[\frac{-d}{a}\] done
clear
B)
\[\frac{c}{a}\] done
clear
C)
\[\frac{-b}{a}\] done
clear
D)
\[\frac{c}{d}\] done
clear
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question_answer52)
If a, p and y are the zeros of p(x), which of the following is true?
A)
\[p(x)=(x-\alpha )(x-\beta )(x-\gamma )\] done
clear
B)
\[p(x)=(x+\alpha )(x-\beta )(x-\gamma )\] done
clear
C)
\[p(x)=(x+\alpha )(x+\beta )(x-\gamma )\] done
clear
D)
\[p(x)=(x+\alpha )(x+\beta )(x+\gamma )\] done
clear
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question_answer53)
Find a quadratic polynomial whose sum and product of zeros are both 1.
A)
\[{{x}^{2}}-x+1\] done
clear
B)
\[{{x}^{2}}-x-1\] done
clear
C)
\[{{x}^{2}}+x-1\] done
clear
D)
\[{{x}^{2}}+x+1\] done
clear
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question_answer54)
The remainder when\[{{x}^{4}}-5x+6\]is divided by\[2-{{x}^{2}}\]is of the form\[px+q\]. What are the respective values of 'p' and 'q'?
A)
10, 5 done
clear
B)
-5, 10 done
clear
C)
-10, 5 done
clear
D)
-10, -5 done
clear
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question_answer55)
Which of the following is not correct?
A)
The degree of a zero polynomial is zero. done
clear
B)
The polynomial\[{{x}^{4}}+1\]has 4 zeros. done
clear
C)
The degree of a cubic polynomial is 3. done
clear
D)
A quadratic polynomial has two zeros. done
clear
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