Given :
One root of a third degree polynomial function f(x) is –5 + 2i.
To Find :
The number and nature of all roots for this function.
Solution :
We know, there are exactly three roots in any third degree polynomial.
Also, we know complex roots always comes in pair i.e. the other root is the conjugate of each other .
So, other root is , -5 - 2i .
Also, since complex roots come in conjugate pair. So, third root cannot be complex.
Therefore, 2 roots are complex and 1 is real.
