Complex Numbers And Quadratic Equations question 547
Question: The quadratic equation whose one root is $ \frac{1}{2+\sqrt{5}} $ will be [RPET 1987]
Options:
A) $ x^{2}+4x-1=0 $
B) $ x^{2}+4x+1=0 $
C) $ x^{2}-4x-1=0 $
D) $ \sqrt{2}x^{2}-4x+1=0 $
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ \alpha =\frac{1}{2+\sqrt{5}} $ and $ \beta =\frac{1}{2-\sqrt{5}} $ Sum of roots $ \alpha +\beta =-4 $ and product of roots $ \alpha \beta =-1 $ Thus required equation is $ x^{2}+4x-1=0 $
BETA
