Polynomial Equations
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. Example: Find all the rational solutions of (2x^{3}  5)/4 = x  x^{2 }
Example
Solve
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.
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