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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.
It is given in the question that,
Zeros of the polynomial x2 – 5x + k are
α- β = 1
Now by using the relationship between the zeros of the quadratic polynomial we have:
Sum of zeros = and product of zeros =
α + β=5 and α β = k/1
Now solving α- β=1 and α + β = 5, we get:
these values in we get: