Complex Numbers And Quadratic Equations question 545
Question: The quadratic equation whose one root is $ 2-\sqrt{3} $ will be [RPET 1985]
Options:
A) $ x^{2}-4x-1=0 $
B) $ x^{2}-4x+1=0 $
C) $ x^{2}+4x-1=0 $
D) $ x^{2}+4x+1=0 $
Show Answer
Answer:
Correct Answer: B
Solution:
Given that first root is $ 2-\sqrt{3} $ , so other root will be $ 2+\sqrt{3} $ . Now the sum of roots is $ 2-\sqrt{3}+2+\sqrt{3}=4 $ and the product of roots $ (2+\sqrt{3})(2-\sqrt{3})=4-3=1 $ Hence required equation is $ x^{2}-4x+1=0 $ .
BETA
