Question

If one of the zero of polynomial f(x)=(K square +4)x square + 13x+4k is reciprocal of the other then find value of k

Answer 1

Let the roots of (k2 + 4) x2 + 13x + 4k be p and 1/p.
Product of the roots = p x 1/p = (constant term) / coefficient of x2
⇒ (4k) / (k2 + 4) = p x 1/p
⇒ (4k) / (k2 + 4) = 1
⇒ k2 - 4k + 4 = 0
⇒ (k - 2)2 = 0
⇒ k - 2 = 0
⇒ k = 2

Answer 2

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