Question

If the zeroes of the polynomial `ax^2+bx+(2a)/b` are reciprocal of each other, then the value of b is ______.

Options

• 2

• `1/2`

• −2

• `-1/2`

Answer 1

If the zeroes of the polynomial `ax^2+bx+(2a)/b` are reciprocal of each other, then the value of b is 2.

Explanation:

Given, `ax^2+bx+(2a)/b`

Let be a quadratic equation Ax² + Bx + C.

Compare both equations, A = a, B = b, C = `(2a)/b`

∴ Product of zeroes = 1  ....(Given)

`C/A = 1`

∵ `(2a)/(b/a) = 1`  ....(Put the values C and A)

`(2a)/b = a`

b = 2