PP Section 2.1 - equation solutions real different two 4 2...

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    Quadratic Equations
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    Definition A quadratic equation has the form 0 , 0 2 = + + a c bx ax x is the variable, a, b, c are real numbers,  called the coefficients. Examples: 0 4 5 2 = + + x x 0 4 3 2 = + - x 0 6 2 2 = - x x 0 3 2 = + - x x
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    How to Solve There are three methods for solving a quadratic  equation:   By factoring   By completing the square   By using the quadratic formula
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    Example Solve the equation below using the three  methods. 0 6 2 = - - x x By factoring: 0 ) 2 )( 3 ( 6 2 = + - = - - x x x x 0 2 OR 0 3 = + = - x x 2 OR 3 - = = x x
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    By completing the square: 0 6 ) ( 6 4 1 4 1 2 2 = - - + - = - - x x x x 0 ) ( 4 25 2 2 1 = - - x 2 5 2 1 ± = - x 2 4 2 6 2 5 2 1 , - = ± = x 2 , 3 - = x
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    Using the quadratic formula: a ac b b x 2 4 2 - ± - = 2 5 1 2 ) 6 ( 4 1 ) 1 ( ± = - - ± - - = x 2 , 3 - = x
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    The Discriminant ac b 4 2 - The discriminant of a quadratic equation is It is used to determine the type of roots of the 
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Unformatted text preview: equation solutions real different two 4 2 ⇒-ac b solution real repeated one 4 2 ⇒ =-ac b solutions real NO 4 2 ⇒ <-ac b Example Determine the number of real solutions for each equation below. 1 2 2 = + + x x 4 4 4 2 =-=-ac b One repeated root. 4 3 2 =-+ x x 25 ) 4 ( 4 9 4 2 =--=-ac b Two different real roots. Comment The roots of a quadratic equation , 2 ≠ = + + a c bx ax Are the x-intercepts of the graph of , 2 ≠ = + + = a c bx ax y...
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This note was uploaded on 01/22/2011 for the course MATH 2 taught by Professor Gardner during the Fall '08 term at Irvine Valley College.

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PP Section 2.1 - equation solutions real different two 4 2...

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