Question

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

• A. $Equal$
• B. $Imaginary$
• C. $Real$
• D. $Noneofthese$

Answer 1

The correct option is C

$Real$

Explanation for correct answer:

Given, $a+b+c=0$ and $4a{x}^2+3bx+2c=0$

For root to be define of quadratic equation then root is given by

$$\begin{gathered} x=\frac{-B{\displaystyle \underset{-}{+}}\sqrt{D}}{2},whereD=B^2-4BAC \\ inthisgivenequation, \\ B=-3b,A=4a,C=2 \end{gathered}$$

$$\begin{gathered} D=9b^2–4\left(4a\right)\left(2c\right) \\ =9{(a+c)}^2–32ac \\ =9{(a–c)}^2+4ac>0 \\ rootsarereal \end{gathered}$$

Hence the correct option is $\left(C\right)$