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  4. If a+b+c=0 , then the roots of the equation 4ax2+3bx+2c=0 are

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Q. If $ a+b+c=0 $ , then the roots of the equation $ 4a{x}^{2}+3bx+2c=0 $ are

ManipalManipal 2008

Solution:

Given, $a+b+c=0$
Let the roots of the equation $4 \,a x^{2}+3\, b x+2\, c=0$ are $\alpha$ and $\beta$
Now, $D=b^{2}-4 \,a c$
$=9 b^{2}-4(4 a)(2 c)$
$=9 b^{2}-32\,a c$
$=9(a+c)^{2}-32 \,a c$
Hence, roots are real.