Q15 of 113 Page 71

If α, 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,

f (x) = x2 – 5x + k such that its coefficients are a = 1, b = - 5 and c = k


∴ =



= 5 (i)


, = 1 (ii)


, we get:


2a = 6


a = = 3


Now putting the value of a in (i), we get


3 + = 5


= 5 – 3 = 2



=


Hence, k = 6


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