11.3-one - 11.3 Solving Equations by Using Quadratic...

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Unformatted text preview: 11.3 Solving Equations by Using Quadratic Methods Solving Quadratic Equations Solving a Quadratic Equation 1) If the equation is in the form (ax + b)2 = 6, use the square root property and solve. If not, go to Step 2. 2) Write the equation in standard form: ax2 + bx + c = 0. 3) Try to solve the equation by the factoring method. If not possible, go to Step 4. 4) Solve the equation by the quadratic formula. Completing the square often involves more complicated computations with fractions, which can be avoided by using the quadratic formula. Solve 12x = 4x2 + 4. Minx + EFT—0 WWW Wax-+1110 Solve the following quadratic equation. 5 1 —wf+m*—=O 8 2 it i E 5m{+%m‘*% 3 &:5 5:8 C: r? X; 4y: bra—ta; 3Q ng#;ﬂ#r#, .5 Ag“ (62—, .aw ,'hﬂﬂf#ﬂ#f#rpﬂ R6“ L##f##f#dﬂ__ m t. ~—~%-i\iiti4 lo 1: m -—%+I?_ reg—i; 10 [D L : The steps we detailed in solving quadratic equations will only work if the equation is in an obviously recognizable form. Sometimes, we may have to alter the form of an equation to get it into quadratic form. This might involve substitution into the equation, squaring both sides of the equation, or converting a rational equation. Solve the following equation r———~ — x/Zx z 4 u— ' *X 1".“ ,s__,. 1 61px ) : (LE AX) X21— LEX‘r—LEX'HG. 5“— ZX 52X" ‘1 Li: W41“? X21 %x He 22% P. _ ax zip—€144 Xﬂmwﬂe :© 0 :: t£.—l®x-erz (x ﬁg) (XV—3k) :0 o a: UAW”) c W3 Z * xxg, 2t Solve the following equation 5 4 RkUZZIfZ. 3C“2+x+2:1 Lth (X’2)U§‘H~) (N (PH-l? 32:. + (kayak) ’4,“ ._._ LX'r—L)CX"H’—) - No UN? 6 [X423 4— we.) :LX'~1)(X+2) D. 5XMO%MX~%=—X—H .71 b1 0 2 ‘Pi—szm é. 0:;1 ._ ~4— 2. X: b—anﬂ—LHAC bc‘ 9‘0‘ Cry—g; 02L!) : Q‘tJ8l+a¢ 3 M? X f a: W?” 21A? °“ 9/3 Y‘s—ﬁt???“ Solve the following equation 9x4 + 5x2 —- 4 = 0 W0 3! m“, nm an-wﬁ—vo 00* X ...
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This note was uploaded on 01/16/2012 for the course MATH 096 taught by Professor Jimcotter during the Fall '11 term at Truckee Meadows Community College.

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11.3-one - 11.3 Solving Equations by Using Quadratic...

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