Question

If the harmonic means of the roots of $\sqrt{2x^2}-bx+8-2\sqrt{5}=0$ is 4,then the value of b=

• A. 2
• B. 3
• C. $4-\sqrt{5}$
• D. $4+\sqrt{5}$

Answer 1

The correct option is C $4-\sqrt{5}$

Let $\alpha ,\beta betheroots$

$\Rightarrow \frac{2\alpha \beta }{\alpha +beta}=4$

$\Rightarrow \frac{\frac{2(8-2\sqrt{5})}{\sqrt{2}}}{\frac{b}{\sqrt{2}}}=4$

$\Rightarrow \frac{2(8-2\sqrt{5})}{4}=b$

$\therefore b=4-\sqrt{5}$