Complex Numbers And Quadratic Equations question 762
Question: If $ a+b+c=0 $ , then the roots of the equation $ 4ax^{2}+3bx+2c=0 $ are
Options:
A) Equal
B) Imaginary
C) Real
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
We have $ 4ax^{2}+3bx+2c=0 $ Let roots are $ \alpha $ and $ \beta $ Let $ D=B^{2}-4AC $ $ =9b^{2}-4(4a)(2c)=9b^{2}-32ac $ Given that, $ (a+b+c)=0\Rightarrow b=-(a+c) $ Putting this value, we get $ =9{{(a+c)}^{2}}-32ac=9{{(a-c)}^{2}}+4ac $ . Hence roots are real.
BETA
