Q. 154.8( 11 Votes )

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

Answer :

It is given in the question that,

f (x) = x^{2} – 5x + k such that its coefficients are a = 1, b = - 5 and c = k

∴ =

= 5 (i)

, = 1 (ii)

, we get:

2α = 6

α = = 3

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

3 + = 5

= 5 – 3 = 2

we know, Product of zeroes

=

Hence, k = 6

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