10th Class Mathematics Polynomials Question Bank

MCQs - Polynomials Total Questions - 45

1)

Which of the following is not a polynomial

A)
\[3x+5\]

B)
\[3{{y}^{3}}-4{{y}^{2}}+2y\]

C)
\[{{x}^{3}}-3\]

D)
\[\frac{1}{x+2}\]
View Solution
2)

If 2 is a zero of polynomial \[f\left( x \right)=a{{x}^{2}}-3\left( a-1 \right)x-1\]then the value of a is

A)
0

B)
2

C)
\[\frac{5}{2}\]

D)
\[\frac{1}{2}\]
View Solution
3)

If one of the zeroes of the quadratic polynomial \[\left( k-1 \right){{x}^{2}}+kx+1\] is \[-3\], then the value of k is

A)
\[\frac{4}{3}\]

B)
\[-\frac{4}{3}\]

C)
\[\frac{2}{3}\]

D)
\[\frac{-2}{3}\]
View Solution
4)

If one of the zeroes of the quadratic polynomial \[{{x}^{2}}+\text{ }3x\text{ }+\text{ }k\] is 2, then the value of k is

A)
10

B)
-10

C)
-7

D)
-2
View Solution
5)

If 2 and 3 are zeroes of polynomial\[3{{x}^{2}}-2kx+2m\], then the values of k and m are

A)
\[m=\frac{9}{2}\] and \[k=15\]

B)
\[m=\frac{15}{2}\] and \[k=9\]

C)
\[m=9\] and \[k=\frac{15}{2}\]

D)
\[m=15\] and \[k=9\]
View Solution
6)

The value of p, for which (-4) is a zero of the polynomial \[{{x}^{2}}-2x\left( 7p+3 \right)\]is

A)
3

B)
2

C)
4

D)
-2
View Solution
7)

If the graph of a polynomial intersects the X-axis at only one point, it can be a

A)
linear

B)
quadratic

C)
cubic

D)
None of these
View Solution
8)

Which of the following is not the graph of a quadratic polynomial?

A)

B)

C)

D)

View Solution
9)

The graph of a quadratic polynomial is ............ .

A)
straight line

B)
parabola

C)
hyperbola

D)
None of these
View Solution
10)

If one zero of polynomial \[{{x}^{2}}-4x+1\] is\[2+\sqrt{3}\], then other zero will be .........

A)
\[-2+\sqrt{3}\]

B)
\[-\sqrt{3}-2\]

C)
\[2-\sqrt{3}\]

D)
\[\sqrt{3}+1\]
View Solution
11)

The zeroes of the quadratic polynomial \[\left( {{x}^{2}}+5x+6 \right)\]are

A)
-2 and -3

B)
3 and 4

C)
3 and 2

D)
2 and 1
View Solution
12)

Zeroes of \[p\left( z \right)={{z}^{2}}-27\]are ............ and ............

A)
\[\pm \,3\sqrt{3}\]

B)
\[+3\]

C)
\[+9\]

D)
\[+\sqrt{3}\] and \[-\sqrt{3}\]
View Solution
13)

The zeroes of the quadratic polynomial\[f\left( x \right)=ab{{x}^{2}}+\left( {{b}^{2}}-ac \right)x-bc\]are

A)
\[\frac{b}{ac}\] and \[\frac{c}{b}\]

B)
\[\frac{ab}{c}\] and \[\frac{a}{b}\]

C)
\[\frac{-b}{a}\]and \[\frac{c}{b}\]

D)
\[\frac{b}{a}\] and \[\frac{-c}{b}\]
View Solution
14)

The number of polynomials having zeroes as - 2 and 5 is

A)
1

B)
2

C)
3

D)
more than 3
View Solution
15)

1 and 2 are the zeroes the polynomial \[{{x}^{2}}-3x+2\]

A)
True

B)
False

C)
Can't say

D)
Partially true/false
View Solution
16)

Every real number is the zeroes of zero polynomial

A)
True

B)
False

C)
Can't say

D)
Partially true/False
View Solution
17)

\[p\left( x \right)=x-1\] and\[g\left( x \right)={{x}^{2}}-2x+1\], \[p\left( x \right)\] is a factor of g (x)

A)
True

B)
False

C)
Can't Say

D)
Partially True/False
View Solution
18)

The value of k for which 3 is a zero of polynomial \[2{{x}^{2}}+x+k\]is ............

A)
21

B)
20

C)
-21

D)
18
View Solution
19)

If zeroes a and P of a polynomial \[{{x}^{2}}-7x+k\]are such that\[\alpha -\beta =1\], then the value of k is

A)
21

B)
12

C)
9

D)
8
View Solution
20)

Sum of zeroes of Quadratic polynomial \[=-\frac{Coefficient\,of\,x}{Coefficient\,of\,{{x}^{2}}}\]

A)
True

B)
False

C)
Can't say

D)
Partially true/false
View Solution
21)

If \[\alpha \] and \[\beta \] are zeroes of the quadratic polynomial \[{{x}^{2}}-6x+a\]the value of 'a', if \[3\alpha +2\beta =20\]is -12

A)
True

B)
False

C)
Can't say

D)
Partially True/False
View Solution
22)

If one of the zeroes of a quadratic polynomial of the form \[{{x}^{2}}+ax+b\]is the negative of the other, then it

A)
has no linear term and the constant term is negative

B)
has no linear term and the constant term is positive

C)
can have a linear term but the constant term is negative

D)
can have a linear term but the constant term is positive
View Solution
23)

If p and q are zeroes of\[3{{x}^{2}}+2x-9\], then value of p - q is

A)
-3

B)
-2

C)
\[\pm \,\frac{4\sqrt{7}}{3}\]

D)
None of these
View Solution
24)

The polynomial whose zeroes are\[\left( \sqrt{2}+1 \right)\] and \[\left( \sqrt{2}-1 \right)\]is

A)
\[{{x}^{2}}+2\sqrt{2}x+1\]

B)
\[{{x}^{2}}-2\sqrt{2}x+1\]

C)
\[{{x}^{2}}+2\sqrt{2}x-1\]

D)
\[{{x}^{2}}-2\sqrt{2}x-1\]
View Solution
25)

If \[\alpha \] and \[\beta \] are the zeroes of the polynomial \[2{{y}^{2}}+7y+5\], then the value of \[\alpha +\beta +\alpha \beta \]is

A)
-1

B)
0

C)
1

D)
2
View Solution
26)

If \[\alpha \] and \[\beta \] are the zeroes of the quadratic polynomial \[f\left( x \right)=3{{x}^{2}}-5x-2\] then \[{{\alpha }^{3}}+{{\beta }^{3}}\] is equal to

A)
\[\frac{215}{27}\]

B)
\[\frac{357}{21}\]

C)
\[\frac{115}{28}\]

D)
\[\frac{325}{31}\]
View Solution
27)

If \[\alpha \]and \[\beta \]are the zeroes of \[4{{x}^{2}}+3x+7\]then the value of \[\frac{1}{\alpha }+\frac{1}{\beta }\]is

A)
\[-\frac{8}{7}\]

B)
\[-\frac{3}{7}\]

C)
\[\frac{2}{7}\]

D)
\[\frac{6}{8}\]
View Solution
28)

If the zeroes of the quadratic polynomial \[{{x}^{2}}+\left( a+1 \right)x+b\]are 2 and - 3, then

A)
\[a=-7,\,b=-1\]

B)
\[a=5,\,b=-1\]

C)
\[a=2,\,b=-6\]

D)
\[a=0,\,b=-6\]
View Solution
29)

If the sum and difference of zeroes of quadratic polynomial are - 3 and - 10, respectively. Then, the difference of the squares of zeroes is

A)
20

B)
30

C)
15

D)
25
View Solution
30)

If sum and product of zeroes of quadratic polynomial are, respectively 8 and 12, then their zeroes are

A)
2 and 6

B)
3 and 4

C)
2 and 8

D)
2 and 5
View Solution
31)

If to and n are the zeroes of the polynomial\[3{{x}^{2}}+11x-4\], then find the value \[\frac{m}{n}+\frac{n}{m}\].

A)
\[\frac{145}{12}\]

B)
\[-\frac{145}{12}\]

C)
\[\frac{145}{7}\]

D)
\[\frac{-145}{15}\]
View Solution
32)

If one zero of the polynomial\[3{{x}^{2}}-8x+2k+1\]is seven times the other, then the value of k is

A)
\[\frac{2}{5}\]

B)
\[\frac{2}{3}\]

C)
\[\frac{2}{7}\]

D)
\[\frac{3}{2}\]
View Solution
33)

If sum of the squares of zeroes of the quadratic polynomial \[f\left( x \right)={{x}^{2}}-4x+k\]is 20, then the value of k is

A)
-2

B)
-3

C)
-4

D)
2
View Solution
34)

If \[\alpha \] and \[\beta \]are zeroes of the polynomial \[{{x}^{2}}-p\left( x+1 \right)+c\]such that \[\left( \alpha +1 \right)\left( \beta +1 \right)=0\], then the value of c is

A)
-2

B)
2

C)
-1

D)
1
View Solution
35)

The value of k such that the polynomial \[{{x}^{2}}-\left( k+6 \right)x+2\left( 2k-1 \right)\]has sum of its zeroes equal to half of their product is

A)
-4

B)
4

C)
-7

D)
7
View Solution
36)

The sum and the product of zeroes of the polynomial \[{{x}^{2}}-\left( k+6 \right)x+2\left( 2k-1 \right)\]are equal the value of k is

A)
k=3

B)
k=-3

C)
\[k=\pm \,3\]

D)
k=2
View Solution
37)

If \[\alpha \] and \[\beta \]are the zeroes of the quadratic polynomial \[f\left( x \right)={{x}^{2}}-4x+3\], then the value of\[{{\alpha }^{4}}{{\beta }^{3}}+{{\alpha }^{3}}{{\beta }^{4}}\] is

A)
104

B)
108

C)
112

D)
5
View Solution
38)

The quadratic polynomial, the sum of whose zeroes is - 5 and their product is 6, is

A)
\[{{x}^{2}}+5x+6\]

B)
\[{{x}^{2}}-5x+6\]

C)
\[{{x}^{2}}-5x-6\]

D)
\[-{{x}^{2}}+5x+6\]
View Solution
39)

The quadratic polynomial whose zeroes are \[2\sqrt{7}\]and \[-5\sqrt{7}\] is

A)
\[{{x}^{2}}-3\sqrt{7}x-70\]

B)
\[{{x}^{2}}+3\sqrt{7}x+70\]

C)
\[{{x}^{2}}+3\sqrt{7}x-70\]

D)
\[{{x}^{2}}-3\sqrt{7}x+70\]
View Solution
40)

The quadratic polynomial, whose zeroes are \[3+\sqrt{2}\]and \[3-\sqrt{2}\], is

A)
\[{{x}^{2}}-3x+5\]

B)
\[{{x}^{2}}-6x+7\]

C)
\[{{x}^{2}}-7x+6\]

D)
\[{{x}^{2}}-8x+12\]
View Solution
41)

If \[\alpha \] and \[\beta \] are the zeroes of the quadratic polynomial \[f\left( x \right)={{x}^{2}}+x-2\], then the polynomial whose zeroes are \[2\alpha +1\]and \[2\beta +1\]is

A)
\[{{x}^{2}}+9\]

B)
\[{{x}^{2}}-4\]

C)
\[{{x}^{2}}-9\]

D)
\[{{x}^{2}}+4\]
View Solution
42)

If \[\alpha \] and \[\beta \] are zeroes of a quadratic polynomial \[{{x}^{2}}-5\], then the quadratic polynomial whose zeroes are \[1+\alpha \] and \[1+\beta \] is

A)
\[{{x}^{2}}+2x+24\]

B)
\[{{x}^{2}}-2x-24\]

C)
\[{{x}^{2}}-2x+24\]

D)
None of these
View Solution
43)

The number of value of k for which the quadratic polynomial \[k{{x}^{2}}+x+k\]has equal zeroes is

A)
4

B)
1

C)
2

D)
3
View Solution
44)

\[p\left( x \right)=5{{x}^{3}}-3{{x}^{2}}+7x+2\], then match the value of Column I with that of

Column I Column II

A. p(1) P. 2

B. p(0) Q. 11

C. p(5) R. -13

D. p(-1) S. -64

E. p(-2) T. 587

A)
A-Q,     B-T,      C-R,      D-P,      E-S

B)
A-Q,     B-R,      C-T,      D-S,      E-P

C)
A-Q,     B-P,      C-T,      D-R,      E-S

D)
A-T,      B-R,      C-Q,     D-S,      E-P
View Solution

If \[\alpha \] and \[\beta \] are the zeroes of the polynomial\[2{{x}^{2}}-4x+5\], then match the value of Column I with that of Column II

	Column I		Column II
A.	\[\frac{1}{\alpha }+\frac{1}{\beta }\]	1.	- 6
B.	\[{{\left( \alpha -\beta \right)}^{2}}\]	2.	\[\frac{-4}{25}\]
C.	\[\frac{1}{{{\alpha }^{2}}}+\frac{1}{{{\beta }^{2}}}\]	3.	\[\frac{-2}{5}\]
D.	\[\frac{\alpha }{\beta }+\frac{\beta }{\alpha }\]	4.	\[\frac{4}{5}\]

A-4, B-1, C-2, D-3

A-4, B-2, C-1, D-3

A-1, B-2, C-3, D-4

A-1, B-4, C-2, D-3

View Solution

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MCQs - Polynomials

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Column I		Column II
A.	p(1)	P.	2
B.	p(0)	Q.	11
C.	p(5)	R.	-13
D.	p(-1)	S.	-64
E.	p(-2)	T.	587

10th Class Mathematics Polynomials Question Bank

done MCQs - Polynomials Total Questions - 45

Study Package

MCQs - Polynomials

MCQs - Polynomials Total Questions - 45