Question

The two equations $x^3+1=0$ and $a{x}^2+bx+c=0,a,b,c\in R$ have two roots in common. Then $a+b$ is equal to

• A. $3$
• B. $2$
• C. $0$
• D. $-1$

Answer 1

The correct option is C $0$

$x^3+1=0\Rightarrow (x+1)(x^2-x+1)=0$
$x^2-x+1=0$ has non-real roots as $\Delta <0$

We know that, for a quadratic equation with real coefficients, imaginary roots always occur in conjugate pair.
$\therefore x^2-x+1=0$ and $a{x}^2+bx+c=0$ have both roots in common.
$\Rightarrow \frac{1}{a}=\frac{-1}{b}=\frac{1}{c}$
$\Rightarrow a+b=0$