Complex Numbers And Quadratic Equations question 763
Question: The roots of the given equation $ 2(a^{2}+b^{2})x^{2}+2(a+b)x+1=0 $ are
Options:
A) Rational
B) Irrational
C) Real
D) Imaginary
Show Answer
Answer:
Correct Answer: D
Solution:
Given equation $ 2(a^{2}+b^{2})x^{2}+2(a+b)x+1=0 $ Let $ A=2(a^{2}+b^{2}),B=2(a+b) $ and $ C=1 $ $ B^{2}-4AC=4(a^{2}+b^{2}+2ab)-4.2(a^{2}+b^{2})1 $
$ \Rightarrow B^{2}-4AC=-4{{(a-b)}^{2}}<0 $ Thus given equation has imaginary roots.
BETA
