In the case of quadratic polynomials , the roots are complex when the discriminant is negative.
Factor completely, using complex numbers.
First, factor out an x .
Now use the quadratic formula for the expression in parentheses, to find the values of x for which .
Here a = 1, b = 10 and c =169.
Write the square root using imaginary numbers.
We now know that the values of x for which the expression
equals 0 are .
So, the original polynomial can be factored as
You can verify this using FOIL .