Question

If a cubic polynomial equation with real coefficients $f\left(x\right)=0$ has one complex root $a+ib,$ then the number of real roots will be .

• A. $1$
• B. $2$
• C. $3$

Answer 1

The correct option is A $1$

The cubic polynomial equation $f\left(x\right)=0$ with real coefficients has one complex root $a+ib.$
Now, we know complex roots always occur in conjugate pair.
$\Rightarrow a-ib$ will be it's second root.
Now, by fundamental theorem of algebra, a cubic polynomial equation will have $3$ roots.
$\Rightarrow f\left(x\right)=0$ will have $1$ real root.