# 2.6 Solving Quadratic Equations with Complex Roots 11/9/2012.

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2.6 Solving Quadratic Equations with Complex Roots 11/9/2012

Completing the square Solve by completing the square. x 2x 2 2x2x3 + 0 = – x 2x 2 2x2x3 + 0 = – 2 = – ()2)2 1x – Take the square root of each side. = 1 x – 2 – – + Add 1 to each side. = x 2 – – + 1 Write in terms of i. = x + – 1 i 2 ANSWER The solutions are and. +1 i 2 1 i 2 – (x 2 – 2x +1) + 3 – 1 = 0 (x – 1) 2 + 2 = 0 Subtract 2 from both sides.

Sum of Squares pattern Find complex solution of x 2 + 49 = 0 x 2 + 49 = 0 - 49 - 49 x 2 = -49 x = -1 49 x = ± 7 i

Sum of Squares pattern Find complex solution of 25x 2 + 9 = 0

Quadratic Formula: Is used to solve quadratic equations written in the form ax 2 + bx +c = 0

Solve an Equation with Imaginary Solutions Solve x 2x 2 2x2x2 ++ 0.0. = x = + – – 2 – 1 2 ( (( ( 4 1 ( ( 2 2 Substitute values in the quadratic formula: a 1, b 2, and c 2. = == 2a2a x = – b + – b 2b 2 – 4ac4ac x = + – – 2 – 4 2 Simplify. Simplify and rewrite using the imaginary unit i. x = + – – 2 2 2i2i + – 1 i ANSWER The solutions are and. – 1 i – Simplify. x = + – – 1 i SOLUTION

Use the quadratic formula to solve the equation. Use the Quadratic Formula 2x 22x 2 x = - 4 - 2a2a x = – b + – b 2b 2 – 4ac4ac

Homework WS 2.6 #1, 2, 4-14even