Math, asked by saramaryam, 9 months ago

anyone knows the answer?

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Answers

Answered by Mihir1001

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$Answer:$

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$\huge\boxed{\fcolorbox{red}{#ffdfff}{q = 8}}$

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$Step-by-step-explaination:$

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let,

$p(x) = {x}^{2} - 6x + q$

let $\alpha$ and $\beta$ be the zeroes of the polynomial p(x).

let,

$\alpha = 2 \beta$

Now,

sum of zeroes $= \alpha + \beta$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \beta + \beta$

$\implies sum \: of \: zeroes = 3 \beta$

$\implies \frac{ - ( - 6)}{(1)} = 3 \beta$

$\implies 3 \beta = 6$

$\implies \beta = 2$

Therefore,

$\alpha = 2 \beta$

$\implies \alpha = 2(2)$

$\implies \alpha = 4$

Now,

Product of zeroes $= \alpha \beta$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (4)(2)$

$\implies \frac{q}{1} = 8$

$\implies q = 8$

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