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MAT 108 Quadratic Equations

MAT 108 Quadratic Equations. By Dr. Marinas. Solving Equations. In sections 1.1 and 1.2, we solved LINEAR equations. This means that the highest exponent is 1. In section 1.3, we will be solving equations with the highest exponent of 2. These are called Quadratic Equations.

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MAT 108 Quadratic Equations

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  1. MAT 108 Quadratic Equations By Dr. Marinas

  2. Solving Equations • In sections 1.1 and 1.2, we solved LINEAR equations. This means that the highest exponent is 1. • In section 1.3, we will be solving equations with the highest exponent of 2. These are called Quadratic Equations.

  3. What are Quadratic Equations? • They are in the form: ax2 + bx + c = 0 • Methods of Solving Quadratic Equations (Put into above form first)? • By Factoring (sometimes works) • By Quadratic Formula (always works)

  4. Put in Standard Form Factor the polynomial Set each factor to 0 Solve for the variable Check answer in original equation x2 - 3x = 4 x2 - 3x - 4 = 0 (x - 4) (x + 1) = 0 x - 4 = 0 or x + 1 = 0 x = 4 or x = -1 42 - 3(4) = 4 (-1)2 - 3(-1) = 4 By Factoring

  5. This method works all the time. It is usually used when the Factoring method fails. Put in standard form. Determine the values of a, b, and c. By Quadratic Formula

  6. The Quadratic Formula _______ -b +  b2 - 4ac • x = ------------------------ 2 a

  7. Example: • x2 + 9x = -8 • Standard form: x2 + 9x + 8 = 0 • We could do this by Factoring but let’s use the Quadratic Formula. • a = 1, b = 9 and c = 8 -9 + 92 - 4(1)(8) -9 + 49 • x = ------------------------ = ----------- 2(1) 2

  8. Example Continues -9 + 49 -9 + 7 x = -------------- = ------- 2 2 • x = (-9-7)/2 or x = (-9 + 7)/2 • x = -8 or x = -1 • x2 + 9x = -8 • Check: (-8)2 + 9(-8) = -8 (-1)2 + 9(-1) = -8

  9. Homework Pages 47-48 • Problems (3-69)* • Multiples of 3

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