Quadratic Equations: Factoring, Square Root Methods.

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Presentation transcript:

Quadratic Equations: Factoring, Square Root Methods

Recall, linear equations, ax + b = 0, we could solve easily For second degree polynomials, we have some increased complexity Quadratic = second degree polynomial – ax 2 + bx + c = 0 Quadrus = Latin for square

Methods to consider A) Factoring (when possible) B) Square Roots (when possible) C) Graphing (tricky, not always precise) D) Quadratic Equation (last resort)

Factoring To solve the problem ax 2 + bx + c = 0, we can factor into (a + b) (c + d = 0, and set each term = 0 – Zero Product Property Example. Solve: 5x x = 0

Example. Solve: 9x 2 + 6x = -6x – 6x 2 Only solve when = 0.

Square Root In some cases, we may have special factors involving squared terms (ax + b) 2 = 0 Remember, to “undue” a squared term, we can use square roots 0, 1, or 2 possible answers

Example. Solve: (3x – 5) 2 = 25 Solutions?

Example. Solve: -(2x – 3) = 0

Imaginary Case Example. Solve: (10x -1) 2 = - 36

Assignment Pg. 93 #1-23 odd