Complex Numbers And Quadratic Equations question 610
Question: If one root of the equation $ x^{2}+px+q=0 $ is $ 2+\sqrt{3} $ , then values of p and q are [UPSEAT 2002]
Options:
A) - 4, 1
B) 4, - 1
C) 2, $ \sqrt{3} $
D) $ -2,-\sqrt{3} $
Show Answer
Answer:
Correct Answer: A
Solution:
One root is $ 2+\sqrt{3} $ , then second root must be $ 2-\sqrt{3}. $
Þ Sum of roots $ =-p=[2+\sqrt{3}+2-\sqrt{3}]=4 $
Þ p = - 4 and product of roots $ =q=(2+\sqrt{3})(2-\sqrt{3}]=4-3=1 $
Þ $ (p,q)=(-4,1) $ .
BETA
