AP EAMCET · Maths · Quadratic Equation
If the harmonic mean of the roots of the equation \(\sqrt{2} \mathrm{x}^2-\mathrm{bx}+(8-2 \sqrt{5})=0\) is 4, then the value of \(b\) is
- A \(3\)
- B \(2\)
- C \(4-\sqrt{5}\)
- D \(4+\sqrt{5}\)
Answer & Solution
Correct Answer
(C) \(4-\sqrt{5}\)
Step-by-step Solution
Detailed explanation
Let the roots be \(\alpha\) and \(\beta\). \(\mathrm{HM} = \frac{2\alpha\beta}{\alpha+\beta}\) From the equation \(\sqrt{2} \mathrm{x}^2-\mathrm{bx}+(8-2 \sqrt{5})=0\): \(\alpha+\beta = -\frac{-\mathrm{b}}{\sqrt{2}} = \frac{\mathrm{b}}{\sqrt{2}}\)…
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