The Rational Root Theorem The Rational Root Theorem gives us a tool to predict the Values of Rational Roots:

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Presentation transcript:

The Rational Root Theorem The Rational Root Theorem gives us a tool to predict the Values of Rational Roots:

List the Possible Rational Roots For the polynomial: All possible values of: All possible Rational Roots of the form p/q:

Find a Root That Works For the polynomial: Substitute each of our possible rational roots into f(x). If a value, a, is a root, then f(a) = 0. (Roots are solutions to an equation set equal to zero!)

Find the Other Roots

Find the Other Roots (con’t) The resulting polynomial is a quadratic, but it doesn’t have real factors. Solve the quadratic set equal to zero by either using the quadratic formula, or by isolating the x and taking the square root of both sides.

Find the Other Roots (con’t) The solutions to the quadratic equation: The three complex roots of the polynomial are: For the polynomial:

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