Q3 of 109 Page 3

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

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