If α and β are the zeros of the polynomial f(x) = x^{2} ‒ 5x + k such that α ‒ β = 1, find the value of k.

It is given in the question that,

Zeros of the polynomial x^{2} – 5x + k are

Also,

α- β = 1

Now by using the relationship between the zeros of the quadratic polynomial we have:

Sum of zeros = and product of zeros =

and

α + β=5 and α β = k/1

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

= 2

these values in we get:

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