10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

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

Correct Answer: B

Solution :

Let \[p\left( x \right)={{x}^{2}}-5\]

For finding the zeroes of p(x), put p(x) = 0.

\[\therefore \,\,\,{{x}^{2}}-5=0\Rightarrow x=\pm 5\]

Let \[\alpha =5\] and \[\beta =-5\]

Now, \[1+\alpha =1+5=6\] and \[1+\beta =1-5=-4\]

Thus, 6 and - 4 are the zeroes of new quadratic polynomial. Therefore the new quadratic polynomial i

\[{{x}^{2}}\] - (sum of zeroes) x + product of zeroes

\[\therefore\] Required polynomial

\[={{x}^{2}}-\left[ 6+\left( -4 \right)x+6\times \left( -4 \right) \right]\]

\[={{x}^{2}}-2x-24\]