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f ( x ) = x 2 – 18 x + 16

Bell Ringer: Find the zeros of each function. 4. f ( x ) = x 2 – 18 x + 16. 5. f ( x ) = x 2 + 8 x – 24. Objectives. Define and use imaginary and complex numbers. Solve quadratic equations with complex roots. x 2 = –144. x 2 = –144. (–12 i ) 2. (12 i ) 2. – 144. – 144.

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f ( x ) = x 2 – 18 x + 16

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  1. Bell Ringer: Find the zeros of each function. 4. f(x) = x2– 18x + 16 5. f(x) = x2+ 8x – 24

  2. Objectives Define and use imaginary and complex numbers. Solve quadratic equations with complex roots.

  3. x2 = –144 x2 = –144 (–12i)2 (12i)2 –144 –144 144i 2 –144 144i 2 –144   –144 144(–1) –144 144(–1) Example 2A: Solving a Quadratic Equation with Imaginary Solutions Solve the equation. Take square roots. Express in terms of i. Check

  4. The discriminant is part of the Quadratic Formula that you can use to determine the number of real roots of a quadratic equation.

  5. Caution! Make sure the equation is in standard form before you evaluate the discriminant, b2 – 4ac.

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