Question

Let $a,b,$ and $c$ be real numbers such that $4a+2b+c=0$ and $ab>0$. Then the equation $a{x}^2+bx+c=0$ has

• A. complex roots
• B. exactly one root
• C. real roots
• D. none of these

Answer 1

Answer: (C)

real roots

Let $f\left(x\right)=a{x}^2+bx+c$

$a,b,c$ are real numbers.

$f\left(2\right)=4a+2b+c$

$f\left(2\right)=0$

Hence, $2$ is a root of $a{x}^2+bx+c=0$

Also, sum of the roots $=-\frac{b}{2a}<0$ (As $ab>0$)

Hence, the other root is negative.

Hence, the equation has two distinct real roots.