Question

If alpha and beta are the zeroes of polynomial f(x)=xsquare-5x+k such that alpha-beta=1. Find the value of k

Answer 1

The correct value of k is 6

Answer 2

Hello dear user ..

Solution ✌✌
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By using the relationship between the zeros of the Polynomial

we have

$sum \: \: of \: zeros \: = \frac{ - ( - coefficient \: \: of \: \: x)}{coefficient \: \: of \: \: {x}^{2} } \\ \\ product \: \: of \: zeros = \frac{constant \: \: term}{coefficient \: \: of \: {x}^{2} } \\ \\ = > \alpha + \beta = \frac{ - ( - 5)}{1} \: \: \: \: and \: \: \alpha \beta = \frac{k}{1} \\ \\ solving \: \: \alpha - \beta = 1 \: \: and \: \: \alpha + \beta = 5 \\ \\ we \: \: get \\ \\ \alpha = 3 \: \: \:and \: \: \beta = 2 \\ \\ \\ \\ substiting \: \: these \: \: values \: \: in \: \: \alpha \beta = \frac{k}{1} \\ \\ we \: \: get \: \: \\ k = 6$
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Hope it's helps you.
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