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in Polynomials by (44.3k points)

If α and β are the zeros of the polynomial f(x) = x2 ‒ 5x + k such that α ‒ β = 1, find the value of k.

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Given: α and β are zeroes of f(x) = x2 ‒ 5x + k

and α – β = 1

We know that,

α + β = Sum of zeros = -(coefficient of x)/(coefficient of x2) = 5

α β = Product of zeros = (constant term)/(coefficient of x2) = k

Now solving α – β = 1 and α + β = 5, we get:

α = 3 and β = 2

Again: α β = k (putting value of α and β)

k = 6.

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