Question

If one zero of the polynomial $f(x)=(k^{2}+4) x^{2}+13x+4k$ is reciprocal of the other, then k=
(a) 2
(b) -2
(c) 1
(d)-1

Answer 1

Answer:

Step-by-step explanation:

SOLUTION :

The correct option is (a) : 2.

Given : α  and 1/α are the zeroes of the  polynomial f(x) =(k² + 4)x² + 13x + 4k

On comparing with ax² + bx + c,

a = k² + 4, b= 13, c = 4k

Product of the zeroes = constant term/ Coefficient of x²

α ×1/α = c/a = 4k/ (k² + 4)

1 = 4k/ (k² + 4)

4k = (k² + 4)

(k² + 4) - 4k = 0

(k² - 4k + 4) = 0

(k)² - 2× k × 2 + (2)² = 0

(k - 2)² = 0

[a² - 2ab + b² = (a-b)²]

k - 2 = 0

k = 2  

Hence, the value of k is 2 .

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

The correct option is (a). 2