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  • If alpha and beta are the zeroes of p(x) such that alpha +beta=24 and alpha-beta=8. Find quadratic polynomial having alpha and beta as its zeroes.​

If alpha and beta are the zeroes of p(x) such that alpha +beta=24 and alpha-beta=8. Find quadratic polynomial having alpha and beta as its zeroes.​

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best_answer

$\alpha$ and $\beta$ are zeroes of $p(x)$ such that

$\alpha+\beta=24$......(1)
$\alpha-\beta=8$.....(2)

adding equation (1) and (2) we get

$\alpha=16

similarly

\beta =8

So now we have

\begin{array}{l} \alpha+\beta=24 \\ \alpha \beta=16 \times 8=128 \end{array}

\begin{aligned} &\text {required polymomial is}\\ &x^{2}-(\text {sum of zeroes}) x+\text {product of zeroes}\\ &=>x^{2}-(24) x+128\\ &=>x^{2}-24 x+128 \end{aligned}

Posted by

avinash.dongre

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