lf a + b + c=0, then the roots of the equation $4{\mathrm{ax}}^2+3\mathrm{bx}+2\mathrm{c}=0$ are

Solution:

 Given, a, + b + c=0 ………………..(i)
and $4{\mathrm{ax}}^2+3\mathrm{bx}+2\mathrm{c}=0$
$\begin{array}{r}\because D=b^2-4ac\\ \therefore D=(3b{)}^2-4(4a\left)\right(2c)\\ =9b^2-32ac\end{array}$
$\begin{array}{r}=9(a+c{)}^2-32ac[\because \text{ from Eq. (i) }]\\ =9(a-c{)}^2+4ac>0\end{array}$
Hence, roots are real.