Question

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Answer 1

Question :-

If α and β are the zeroes of the polynomial f(x) = x^2-x-k Such that α - β = 9, find k.

Solution :-

Given Polynomial - x^2-x-k

So,

α + β = -b/a = 1/1 = 1 ......(1)

αβ = c/a = -k ........(2)

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Also,

α - β = 9 (given) .......(3)

From (1) and (3),

β = -8/2

β = -4

Substituting β in (1),

α + β = 1

α + (-4) = 1

α = 1 + 4

α = 5

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From (3),

αβ = -k

5(-4) = -k

-20 = -k

k = 20