Question

If one zero of the polynomial f (x) = (k² + 4) x² + 13x + 4k is reciprocal of the other, then k =
A. 2
B. – 2
C. 1
D. – 1

Answer 1

ismein aapko ke ki jagah-2 rakhna haiaise hi aapke Sare answer nikal jaenge

Answer 2

A. 2

Step-by-step explanation:

Given: Polynomial f (x) = (k² + 4) x² + 13x + 4k  

α and β are the zeroes of the polynomial such that β = 1/α

Sum of zeroes = -b/a = -13/ (k² + 4) = α + 1/α

Product of zeroes = c/a = 4k/(k² + 4) = α * 1/α = 1

4k/(k² + 4) = 1

(k² + 4) = 4k

 k² -4k + 4 = 0

 k² -2k -2k +4 =0

 k(k-2) -2(k-2) = 0

 (k-2)(k-2) = 0

 k = 2

Option A is the answer.