So far we have learned how to find the roots of a polynomial equation. If we have an equation that involves only polynomials we follow the steps:
Step 1. Bring all the terms over to the left hand side of the equation so that the right hand side of the equation is a 0.
Step 2. Get rid of denominators by multiplying by the least common denominator.
Step 3. If there is a common factor for all the terms, factor immediately. Otherwise, multiply the terms out.
Step 4. Use a calculator to locate roots.
Step 5. Use the Rational Root Theorem and synthetic division
to exactly determine the roots.
Find all the rational solutions of
(2x3 - 5)/4 = x - x2
which has no rational roots. Hence the rational root is -3/2 and using the calculator we see that the irrational root is 0.198.