AP EAMCET · Maths · Quadratic Equation
If the harmonic mean between the roots of \((5+\sqrt{2}) x^2-b x+(8+2 \sqrt{5})=0\) is 4 , then the value of \(b\) is
- A \(2\)
- B \(3\)
- C \(4-\sqrt{5}\)
- D \(4+\sqrt{5}\)
Answer & Solution
Correct Answer
(D) \(4+\sqrt{5}\)
Step-by-step Solution
Detailed explanation
Given equation is \[ (5+\sqrt{2}) x^2-b x+(8+2 \sqrt{5})=0 \] Let \(\alpha\) and \(\beta\) be the roots of this equation. \[ \therefore \] \[ \begin{aligned} \alpha+\beta & =\frac{b}{5+\sqrt{2}} \\ \alpha \beta & =\frac{8+2 \sqrt{3}}{5+\sqrt{2}} \end{aligned} \] Given that…
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