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2.6 Solving Quadratic Equations with Complex Roots

2.6 Solving Quadratic Equations with Complex Roots. 11/9/2012. –. 2. +. –. –. x 2. 2 x. 3. 0. +. –. =. +. Add 1 to each side. 2. x. 1. =. –. +. –. –. x 2. 2 x. 3. 0. +. =. Write in terms of i. x. i. 2. 1. =. The solutions are and. ANSWER. –.

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2.6 Solving Quadratic Equations with Complex Roots

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  1. 2.6 Solving Quadratic Equations with Complex Roots 11/9/2012

  2. – 2 + – – x2 2x 3 0 + – = + Add 1 to each side. 2 x 1 = – + – – x2 2x 3 0 + = Write in terms of i. x i 2 1 = The solutions are and . ANSWER – i i 1 1 + 2 2 ( )2 – – 2 x 1 = Completing the square Solve by completing the square. (x2 – 2x+1) + 3 – 1 = 0 (x – 1) 2 + 2 = 0 Subtract 2 from both sides. – Take the square root of each side. 1 x = = =

  3. Sum of Squares pattern Find complex solution of x2 + 49 = 0 x2 + 49 = 0 - 49 - 49 x2 = -49 x = -1 • 49 x = ± 7i

  4. Sum of Squares pattern Find complex solution of 25x2 + 9 = 0 25x2 + 9 = 0 - 9 - 9 25x2 = -9 25 25 x2= - x = x = ± i

  5. Is used to solve quadratic equations written in the form ax2 + bx +c = 0 Quadratic Formula:

  6. x2 2x 2 0. + + = – x 1 Simplify. i = + + + + + – – – – – The solutions are and . ANSWER – – b2 b 4ac ( x = ( 2 1 2a – – – + 1 1 i i Substitute values in the quadratic formula: a1, b 2, and c2. ( ( – – ( ( 4 1 2 2 22 x = = = = – – 4 2 Simplify. x = 2 Solve an Equation with Imaginary Solutions Solve SOLUTION – 2 2i Simplify and rewrite using the imaginary unit i. x = 2

  7. + – - x 2x2 - 4 = – – b2 b 4ac x = 2a Use the Quadratic Formula Use the quadratic formula to solve the equation. Rewrite in standard form: 2x2 – x + 4 = 0 x = x = x = x =

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

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