2 - 1/6/2010 Problem: A room is 4m longer than it is wide....

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1/6/2010 1 Problem: A room is 4m longer than it is wide. The area or the room is 20m 2 . What is the area of the room? Let x be the width of the room. Then the area of the room is x ( x + 4) = x 2 + 4x Equating this to the given area gives x 2 + 4x = 20 Rearranging gives x 2 + 4x–20 = 0 This is a “root finding” problem. Root Finding Problems: General form: find x such that f ( x ) = 0 The values of x for which f ( x ) = 0 are the roots of f ( x ) c bx ax x f ) ( 2 For our problem f ( x ) happens to be a quadratic . The roots can be found using the quadratic formula. a ac b b x x roots 2 4 , 2 2 1 In general there are two roots. One is obtained by using + in the formula and the other by using . If the quantity under the square root is zero the roots are equal. If this quantity is negative the roots are complex numbers.
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1/6/2010 2 Casio Calculator Note Casio calculators can solve quadratics. Hit Mode until menu include “EQN”. Then select this option. Use the right arrow to move from “Unknowns?” to “Degree?” Enter 2 (a quadratic is a second degree polynomial) Enter values for a , b , and c (hit “=“ after each value) Use the up and down arrows to move between the two solutions. If the roots are complex numbers shift plus “=“ toggles between the real and imaginary parts of each solution. If the roots are real this key combination has
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2 - 1/6/2010 Problem: A room is 4m longer than it is wide....

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