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Bell Ringer: Find the zeros of each function.
4. f(x) = x2 – 18x + 16 5. f(x) = x2 + 8x – 24
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Objectives Define and use imaginary and complex numbers.
Solve quadratic equations with complex roots.
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Example 2A: Solving a Quadratic Equation with Imaginary Solutions
Solve the equation. Take square roots. Express in terms of i. Check x2 = –144 –144 (12i)2 144i 2 144(–1) x2 = –144 –144 144(–1) 144i 2 (–12i)2
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The discriminant is part of the Quadratic Formula that you can use to determine the number of real roots of a quadratic equation.
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Make sure the equation is in standard form before you evaluate the discriminant, b2 – 4ac.
Caution!
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