Find a quadratic polynomial, the sum and product of whose zeroes are $-8$ and $12$ respectively. Hence find the zeroes.

Given: A quadratic polynomial, the sum and product of whose zeroes are $-8$ and $12$ respectively.

To do: To find the zeroes.

Solution:

Let $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial.

As given,

The sum of the zeroes$=\alpha+\beta=-8$

Product of the zeroes$=\alpha\beta=12$

The quadratic polynomial:

$x^2-( \alpha+\beta)x+\alpha\beta=0$

$\Rightarrow x^2-( -8)x+12=0$

$\Rightarrow x^2+8x+12=0$

Thus, the quadratic polynomial is $x^2+8x+12=0$.

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Updated on: 10-Oct-2022

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