Question

If one zero of the polynomial is reciprocal of the other find the value of k

Answer 1

Sol: 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 Therefore, the value of k is 2.

Answer 2

Answer:

2

Step-by-step explanation:

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 Therefore, the value of k is 2.