Question

What are the possible numbers of positive real, negative real, and complex zeros of f(x) = 6x3 − 3x2 + 5x + 9?

Answer 1

For this type of third-degree equation, there are also three possible roots. These roots could be real or imaginary. Real roots are whole numbers or fractions. Imaginary roots are those with the term 'i' which is equal to √-1. These are complex numbers.

It is easier to solve this equation by using the scientific calculator under MODE EQN. Choose the form ax3 + bx2 + cx +d = 0. Then substitute a=6, b=-3, c=5 and d=9. The resulting roots are:

x = -0.8 (negative real)
x = 0.65 +1.2i (complex)
x = 0.65 - 1.2i (complex)