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Module :MA0001NP Foundation Mathematics Lecture Week 9

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Quadratic equations

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Solving a Quadratic Equation by factorization by graphical method by quadratic equation formula by using completing square

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By factorization roots (solutions)

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By graphical method x y O roots

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Solving a Quadratic Equation by the quadratic Formula

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By quadratic equation

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a =b =c =110-7

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Solving a Quadratic Equation by Completing the Square

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Nature of Roots

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In general, a quadratic equation may have : (1) two distinct (unequal) real roots (2) one double (repeated) real root (3) no real roots

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Two distinct (unequal) real roots x-intercepts

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One double (repeated) real roots x-intercept

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No real roots no x-intercept

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△ = b 2 - 4ac Since the expression b 2 - 4ac can be used to determine the nature of the roots of a quadratic equation in the form ax 2 – bx + c = 0, it is called the discriminant of the quadratic equation.

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Two distinct (unequal) real roots x-intercepts △ = b 2 - 4ac > 0

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One double (repeated) real roots x-intercept △ = b 2 - 4ac = 0

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No real roots no x-intercept △ = b 2 - 4ac < 0

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1. Solve the following quadratic equation using factorization method, a. 6x² + 5x – 4 =0 b. x² + 3x – 18 = 0 2. Find the nature of roots of the given quadratic equation a. 2x² - 3x – 7 =0 b. - x² - 2x +6 =0 3. Solve the given quadratic equation by using formula, a. X² - 6 x +10 = 0 b. 2x² + 4x + 1 = 0

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4.Solve each equation by completing the square (a)2x 2 + 13x + 20 = 0(b)3x 2 = 4x + 7 (c)x 2 – 8x + 9 = 0(d)-5x 2 + 6x + 1 = 0

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