GUADRATIC EQUATION

May 29th, 2015
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Any equation of type ax2 + bx + c = 0 where a, b, and c are constants and a <> 0, is in standard form for aquadratic equation. Quadratic equations of type ax2 + bx + c = 0 and ax2 + bx = 0 (c is 0) can be factored to solve for x. Examples:

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GUADRATIC EQUATIONAny equation of typeax2+ bx + c = 0wherea,b, andcare constants anda <> 0, is in standard form for aquadratic equation.Quadratic equations of typeax2+ bx + c = 0andax2+ bx = 0(cis0) can be factored to solve forx. Examples:1. Problem: Solve 3x2 + x - 2 = 0 for x. Solution: Factor. (3x - 2)(x + 1) = 0 Use the principle of zero products, which says, if ab = 0, either a, b, or both must be equal to zero. 3x - 2 = 0, x + 1 = 0 3x = 2 , x = -1 x = (2/3) x = -1, (2/3)2. Problem: Solve 3x2 + 5x = 0 for x. Solution: Factor. x(3x + 5) = 0 Use the principle of zero products. x = 0, 3x + 5 = 0 3x = -5 x = -(5/3) x = 0, -(5/3)Quadratic equations of typeax2+ c = 0can be solved by solving forx. Example:3. Problem: Solve 3x2 = 6 for x.Solution: Recognize that the equation is quadratic because it is the same as 3x2 - 6 = 0. Divide each side by 3. x2 = 2 Take the square root of each side. x = SQRT(2), -(SQRT(2))Many times you will come across quadratic equations that are not easy to factor or solve. In those cases, there is a special formula called thequadratic formulathat you can use to solve any quadratic equation.The solutions of

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