# How to find the roots of polynomial equation #2x^3+2x^2-19x+20=0#?

##### 1 Answer

Solution set is

#### Explanation:

**NOTE: I WROTE THIS ANSWER THINKING THE QUESTION WAS TO SOLVE FOR #x#, NOT JUST TO FIND THE ROOTS**

**Step 1: List the possible factors of this equation**

This will be done using the rational root theorem, which states that the factors of

Therefore, our possible factors are given by

**Step 2: Check these factors using the remainder theorem**

This is when the trial and error process comes into play. The remainder theorem is useful because you can check the remainders without actually having to do the division.

It states that if

**Step 3: Use long division to simplify the equation**

We have now found one root. We're not quite certain of the others yet. We can now simplify the equation to a quadratic by using long division or synthetic division.

According, to the table above, the quotient is

#x = (-(-6) +- sqrt((-6)^2 - 4(2)(5)))/(2(2))#

#x = (6 +- sqrt(-4))/4#

#x = (6 +- 2sqrt(-1))/4#

We now use the identity

#x = (6 +- 2i)/4#

#x = (3 +- i)/2#

Hopefully this helps!