Choose the correct answer from the given four options in the following questions:A quadratic polynomial, whose zeroes are $-3$ and 4 , is(A) $x^{2}-x+12$(B) $x^{2}+x+12$(C) $\frac{x^{2}}{2}-\frac{x}{2}-6$(D) $2 x^{2}+2 x-24$

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Given:

Zeroes of a polynomial are $-3$ and $4$.

To do:

We have to find the quadratic polynomial whose zeroes are $-3$ and 4.

Solution:

As given zeroes of a polynomial are $-3$ and $4$.

Sum of the zeroes$=-3+4=1$

Product of the roots $=-3\times4=-12$

Thus, the polynomial is:

$p( x)=x^2-( \text { sum of the zeroes })x+ ( \text { product of the zeroes })$

$\Rightarrow p(x)=x^2-(1)x+(-12)$

$\Rightarrow p(x)=x^2-x-12$

We know that, if we multiply or divide any polynomial by any constant, then the zeroes of the polynomial do not change.

$\Rightarrow p(x)=\frac{x^2}{2}-\frac{x}{2}-\frac{12}{2}$

$\Rightarrow p(x)=\frac{x^2}{2}-\frac{x}{2}-6$

Updated on 10-Oct-2022 13:27:08