Question

If $x^2+x+1$ is a factor of ${ax}^3+b{x}^2+cx+d$, then the real root of ${ax}^3+b{x}^2+cx+d=0$ is

• A. $-\frac{d}{a}$
• B. $\frac{d}{a}$
• C. $\frac{a}{d}$
• D. None of these

Answer 1

Answer: (A)

$-\frac{d}{a}$

If $x^2+x+1$ is a factor of ${ax}^3+b{x}^2+cx+d$
then $a{x}^3+b{x}^2+cx+d=(x^2+x+1)(ax+d)$
Thus required real roots is $ax+d=0\Rightarrow x=-\frac{d}{a}$