Complex Numbers And Quadratic Equations question 586
Question: The harmonic mean of the roots of the equation $ (5+\sqrt{2})x^{2}-(4+\sqrt{5})x+8+2\sqrt{5}=0 $ is [IIT 1999; MP PET 2000]
Options:
A) 2
B) 4
C) 6
D) 8
Show Answer
Answer:
Correct Answer: B
Solution:
Given equation is $ (5+\sqrt{2})x^{2}-(4+\sqrt{5})x+8+2\sqrt{5}=0 $ Hence $ x_1+x_2=\frac{4+\sqrt{5}}{5+\sqrt{2}} $ and $ x_1x_2=\frac{8+2\sqrt{5}}{5+\sqrt{2}}=\frac{2(4+\sqrt{5})}{5+\sqrt{2}}=2(x_1+x_2) $ Harmonic mean $ =\frac{2x_1x_2}{x_1+x_2}=\frac{2x_1x_2}{x_1x_2/2}=4 $ .
BETA
