Question

If the zeroes of the polynomial ${\displaystyle a{x}^2+bx+\frac{2a}{b}}$ are reciprocal of each other, then the value of b is ______.

विकल्प

• 2

• ${\displaystyle \frac{1}{2}}$

• −2

• ${\displaystyle -\frac{1}{2}}$

Answer 1

If the zeroes of the polynomial ${\displaystyle a{x}^2+bx+\frac{2a}{b}}$ are reciprocal of each other, then the value of b is 2.

Explanation:

P(x) = ${\displaystyle a{x}^2+bx+\frac{2a}{b}}$

⇒ ${\displaystyle \alpha .\frac{1}{\alpha }=\frac{c}{a}}$

⇒ 1 = ${\displaystyle \frac{\frac{2a}{b}}{\frac{a}{1}}}$

⇒ ${\displaystyle \frac{1}{1}=\frac{2}{b}}$

⇒ b = 2