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If one zero of the polynomial f (x) = (k2 + 4) x2 + 13x + 4k is reciprocal of the other, then k =
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