# If one zero of the polynomial f (x) = (k2 + 4) x2 + 13x + 4k is reciprocal of the other, then k =A. 2B. – 2C. 1D. – 1

Given;

f(x) = (k2 + 4) x2 + 13x + 4k,

One zero of the polynomial is reciprocal of the other,

Let a be the one zero,

The other zero will be 1/a

As we know that,

Product of the zeros = c/a = 4k/k2 + 4

4k/k2 + 4 = 1

4k = k2 + 4

k2 + 4 – 4k = 0

(k – 2)2 = 0

k = 2

So the value of k is 2

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