Question

please solve this question

Answer 1

Given ::- (a²+9)x²+ 13x +6a = 0

Roots are α and 1/α

Solution ::-

comparing the given equation with ax² + bx + c = 0

a = (a²+9) , b = 13 c = 6a

α + 1/α = -b/a

α² + 1 / α = - 13 / (a² + 9)

α × 1/α = c/a

1 = 6a / (a² + 9)

(a² + 9) = 6a

a² - 6a + 9 = 0

By factorisation method,

a² -3a -3a + 9 = 0

a ( a - 3 ) -3 (a - 9) = 0

(a - 3) (a - 9) = 0

So, a = 3 or a = 9

Therefore, the value of a is 3 or 9.

HOPE IT HELPS YOU!!