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Unformatted text preview: Quadratic Equation Standard form: , Where a does not equal 0. Note that in Tutorial 14: Linear Equations in One Variable , we learned that a linear equation can be written in the form ax + b = 0 and that the exponent on the variable was 1. Note that the difference is the highest exponent on the variable on the quadratic equation is 2. We are going to talk about four ways to solve quadratics. Solving Quadratic Equations by Factoring You can solve a quadratic equation by factoring if, after writing it in standard form, the quadratic expression factors. Step 1: Simplify each side if needed. olve things like removing ( ), removing fractions, adding like terms, etc. To remove ( ): Just use the distributive property. To remove fractions: Since fractions are another way to write division, and the inverse of divide is to multiply, you remove fractions by multiplying both sides by the LCD of all of your fractions. Step 2 : Write in standard form, , if needed. If it is not in standard form, move any term(s) to the appropriate side by using the addition/subtraction property of equality. Also, make sure that the squared term is written first left to right, the x term is second and the constant is third and it is set equal to 0. Step 3 : Factor. If you need a review on factoring go to Tutorial 7: Factoring Polynomials . Step 4: Use the ZeroProduct Principle. If ab = 0, then a = 0 or b = 0 . 0 is our magic number because the only way a product can become 0 is if at least one of its factors is 0. You can not guarantee what the factors would have to be if the product was set equal to any other number. For example if ab = 1, then a = 5 and b = 1/5 or a = 3 and b = 1/3, etc. But with the product set equal to 0, we can guarantee finding the solution by setting each factor equal to 0. That is why it is important to get it in standard form to begin with. Step 5: Solve for the linear equation(s) set up in step 4. If a quadratic equation factors, it will factor into either one linear factor squared or two distinct linear factors. So, the equations found Example 1 : Solve by factoring. View a video of this example Step 1: Simplify each side if needed. This quadratic equation is already simplified. Step 2 : Write in standard form, , if needed. This quadratic equation is already in standard form. Step 3 : Factor . *Quad. eq. in standard form * Factor the trinomial Step 4: Use the ZeroProduct Principle AND Step 5: Solve for the linear equation(s) set up in step 4. *Use ZeroProduct Principle *Solve the first linear equation *Solve the second linear equation There are two solutions to this quadratic equation: x = 5 and x = 2. Example 2 : Solve by factoring. View a video of this example Step 1: Simplify each side if needed....
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This note was uploaded on 02/18/2011 for the course MATH 101 taught by Professor Kindle during the Spring '11 term at South Texas College.
 Spring '11
 Kindle
 Algebra, Linear Equations, Equations

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