Question

if alpha and beta are the zero of polynomial X2-5x-1 then find the value of
$alpha {}^{2} \times beta + alpha \times \: beta {}^{2}$
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Answer 1

★$\huge\bf{\blue{\underline{Question:-}}}$

if alpha and beta are the zeroes of the polynomial x2-5x+k, such that alpha-beta=1, find the value of k

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★$\huge\bf{\red{\underline{Answer:-}}}$

k=6

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★$\huge\bf{\green{\underline{Explanation:-}}}$

alpha and beta are zeros of the polynomial f(x)=x^2-5x+k.

let alpha=a &beta=b

a+b=-(-5/1)=5;ab=k/1=k

Now, a-b=1

squaring both sides

(a-b)^2=1

(a+b)^2-4ab=1

25-4k=1

4k=24

k=6.

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Answer 2

$\huge \tt \pink {answer}$

alpha and beta are zeros of the polynomial f(x)=x^2-5x+k.

let alpha=a &beta=b

a+b=-(-5/1)=5;ab=k/1=k

Now, a-b=1

squaring both sides

(a-b)^2=1

(a+b)^2-4ab=1

25-4k=1

4k=24

k=6.