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Published byStanley Parsons Modified over 4 years ago

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Solving Quadratic Equations (finding roots)

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Example f(x) = x 2 - 4 By Graphing Identifying Solutions Solutions are -2 and 2.

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EXAMPLE 3 Solve a quadratic equation in standard form Solve 2x 2 + 20x – 8 = 0 by completing the square. SOLUTION Write original equation. 2x 2 + 20x – 8 = 0 Add 8 to each side. 2x 2 + 20x = 8 Divide each side by 2. x 2 + 10x = 4 Add 10 2 2, or 5 2, to each side. x 2 + 10x + 5 2 = 4 + 5 2 Write left side as the square of a binomial. (x + 5) 2 = 29

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Solving Quadratic Equations by Factoring

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Solve by using he zero product property. 1)2)3)

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To solve a quadratic equation if you can’t factor the equation: Make sure the equation is in the general form. Identify a, b, and c. Substitute a, b, and c into the quadratic formula: Simplify.

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Solve a previous problem using the quadratic formula.

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Descriminants can give us hints…

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For the equation...... the discriminant There are no real roots as the function is never equal to zero The Discriminant of a Quadratic Function If we try to solve, we get The square of any real number is positive so there are no real solutions to Roots, Surds and Discriminant

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Complex Conjugates and Division Complex conjugates-a pair of complex numbers of the form a + bi and a – bi where a and b are real numbers. ( a + bi )( a – bi ) a 2 – abi + abi – b 2 i 2 a 2 – b 2 ( -1 ) a 2 + b 2 The product of a complex conjugate pair is a positive real number.

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Ex. Find the real and non-real roots of

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