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 $

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.

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

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

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Updated on: 10-Oct-2022

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