Question

The H.M. of the roots of the equation $(5+\sqrt{2})x^2-(4+\sqrt{5})x+(8+2\sqrt{5})=0$ is

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

Answer: (B)

4

Let $\alpha$ and $\beta$ are the roots of given quadratic equation,

so H.M of $\alpha$, $\beta$ $=$ $\frac{2\alpha .\beta }{\alpha +\beta }$ $=$$\frac{2.\left(c/a\right)}{(-b/a)}$, where a,b,c are quadratic equation coefficients

$=$$\frac{-2c}{b}$ $=$$\frac{2.(8+2.\sqrt{5})}{(4+\sqrt{5})}$ $=$ 4.

Hence, option 'B' is correct.