If one zero of the polynomial f (x) = (k^{2} + 4) x^{2} + 13x + 4k is reciprocal of the other, then k =

Given;

f(x) = (k^{2} + 4) x^{2} + 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/k^{2} + 4

∴ 4k/k^{2} + 4 = 1

⇒ 4k = k^{2} + 4

⇒ k^{2} + 4 – 4k = 0

⇒ (k – 2)^{2} = 0

⇒ k = 2

So the value of k is 2

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