# 7.4 Solving Polynomial Equations Objectives: Solve polynomial equations. Find the real zeros of polynomial functions and state the multiplicity of each.

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7.4 Solving Polynomial Equations Objectives: Solve polynomial equations. Find the real zeros of polynomial functions and state the multiplicity of each. functions and state the multiplicity of each. Standard: 2.8.11.N. Solve linear, quadratic and exponential equations.

b.2x 3 + x 2 – 6x = 0

c.5x 3 – 12x 2 + 4x = 0 Some polynomial equations have factors (and roots) that occur more than once.

* b. x 3 + 2x 2 – 4x – 8 = 0

* c. x 3 + 3x 2 – 4 = 0

If x – r is a factor that occurs m times in the factorization of a polynomial expression, P, then r is a root with multiplicity m of the related polynomial equation, P = 0. In example 2 above, 3 is a root with multiplicity 2 of the equation x 3 - 7x 2 + 15x – 9 = 0. When r is a root with even multiplicity, then the graph of the related function will touch but not cross the x-axis at (r, 0). Sometimes polynomials can be factored by using variable substitution.

* x 4 – 9x 2 + 14 = 0

* x 4 – 5x 2 – 6 = 0

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