131 1.4 Quadratic Equations Simplify each power of i. See Example 7. 89. i25 90. i29 91. i22 92. i26 93. i23 94. i27 95. i32 96. i40 97. i -13 98. i -14 99. 1 i -11 100. 1 i -12 Work each problem. 101. Show that 22 2 + 22 2 i is a square root of i. 102. Show that - 22 2 - 22 2 i is a square root of i. 103. Show that 23 2 + 1 2 i is a cube root of i. 104. Show that - 23 2 + 1 2 i is a cube root of i. 105. Show that -2 + i is a solution of the equation x2 + 4x + 5 = 0. 106. Show that -2 - i is a solution of the equation x2 + 4x + 5 = 0. 107. Show that -3 + 4i is a solution of the equation x2 + 6x + 25 = 0. 108. Show that -3 - 4i is a solution of the equation x2 + 6x + 25 = 0. A quadratic equation is defined as follows. 1.4 Quadratic Equations ■ The Zero-Factor Property ■ The Square Root Property ■ Completing the Square ■ The Quadratic Formula ■ Solving for a Specified Variable ■ The Discriminant Quadratic Equation in One Variable A quadratic equation is an equation that can be written in the form ax2 +bx +c =0, where a, b, and c are real numbers and a≠0. The given form is called standard form. A quadratic equation is a second-degree equation—that is, an equation with a squared variable term and no terms of greater degree. x2 = 25, 4x2 + 4x - 5 = 0, 3x2 = 4x - 8 Quadratic equations The Zero-Factor Property When the expression ax2 + bx + c in a quadratic equation is easily factorable over the real numbers, it is efficient to factor and then apply the following zero-factor property. Zero-Factor Property If a and b are complex numbers with ab = 0, then a = 0 or b = 0 or both equal 0.
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