Sequences And Series Ques 8
- The harmonic mean of the roots of the equation $(5+\sqrt{2}) x^2-(4+\sqrt{5}) x+8+2 \sqrt{5}=0$ is
(1999, 2M)
(a) $2$
(b) $4$
(c) $6$
(d) $8$
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Answer:
Correct Answer: 8.(b)
Solution: (b) Let $\alpha, \beta$ be the roots of given quadratic equation. Then,
$ \alpha+\beta=\frac{4+\sqrt{5}}{5+\sqrt{2}} \quad \text { and } \quad \alpha \beta=\frac{8+2 \sqrt{5}}{5+\sqrt{2}} $
Let $H$ be the harmonic mean between $\alpha$ and $\beta$, then
$ H=\frac{2 \alpha \beta}{\alpha+\beta}=\frac{16+4 \sqrt{5}}{4+\sqrt{5}}=4 $
BETA
