Question

Given that the complex number $z=-2+7i$ is a root to the equation: $z^3+6z^2+61z+106=0$
find the real root to the equation.

• A. $z=2$
• B. $z=-2$
• C. $z=-1$
• D. none of these

Answer 1

The correct option is B $z=-2$

Since complex roots are conjugate in pair

So roots are $-2+7i,-2-7i,x$(let)

Product of roots $=(-2+7i)(-2-7i)\left(x\right)=-106⟹3x=-106x=-2$