Obj: To solve equations using the Rational Root Theorem.

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Presentation transcript:

Obj: To solve equations using the Rational Root Theorem

We have learned many methods of solving polynomial equations. Another method, The Rational Root Theorem, involves analyzing one or more integer coefficients of the polynomial in the equation.

Consider: x 3 – 5x 2 - 2x + 24 = 0 and the equivalent equation (x +2)(x – 3)(x – 4) = 0 The roots are _____, _____, and _____. The product of these roots is ________. Notice: All the roots are factors of the ____________. In general, if the coefficients (including the constant term) in a polynomial equation are integers, then any integer root of the equation is a factor of the ________ term.

A similar pattern applies to rational roots. Remember: A rational number is one that can be written as the quotient of two integers. The roots are _______, _______, and _______. The numerators,1, 2, 3 are all factors of the constant term, _______. The denominators 2, 3, 4 are all factors of the leading coefficient, _______.

Also, the real number zeros of a polynomial function are either rational or irrational.

Finding Rational Roots 1.Find the rational roots of x 3 + x 2 – 3x – 3 = 0 a) List the possible rational roots b) Test each possible rational root---look for a remainder of 0.

2) Find the possible rational roots of x 3 – 4x 2 - 2x + 8 = 0

Use the Rational Root Theorem to find all the roots. 1.List the possibilities 2.Test until you find one 3.Write quotient 4.Factor to find the remaining roots 1. Find the roots of x 3 -2x 2 – 5x + 10 = 0

2. Find the roots of 3x 3 + x 2 –x + 1 = 0

x 4 + x 3 + x 2 - 9x – 10 = 03. Find the roots of:

Closure: If a polynomial equation has integer coefficients, how can you find any rational roots the equation might have? Apply the Rational Root Theorem and test each possible root.