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11.1 Solving Quadratic Equations by the Square Root Property

11.1 Solving Quadratic Equations by the Square Root Property. Solving Quadratic Equations by the Square Root Property. Slide 11.1- 2. Review the zero-factor property. Objective 1 . Slide 11.1- 3. Review the zero-factor property. Slide 11.1- 4. CLASSROOM EXAMPLE 1.

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11.1 Solving Quadratic Equations by the Square Root Property

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  1. 11.1 Solving Quadratic Equations by the Square Root Property

  2. Solving Quadratic Equations by the Square Root Property Slide 11.1- 2

  3. Review the zero-factor property. Objective 1 Slide 11.1- 3

  4. Review the zero-factor property. Slide 11.1- 4

  5. CLASSROOM EXAMPLE 1 Solving Quadratic Equations by the Zero-Factor Property Solution: Solve each equation by the zero-factor property. 2x2−3x + 1 = 0 x2 = 25 Slide 11.1-6

  6. Objective 2 Solve equations of the form x2 = k, where k >0. Slide 11.1-7

  7. Square Root Property If k is a positive number and if x2 = k, then or The solution set is which can be written (± is read “positive or negative” or “plus or minus.”) When we solve an equation, we must find all values of the variable that satisfy the equation. Therefore, we want both the positive and negative square roots of k. Solve equations of the form x2 = k, where k> 0. We might also have solved x2 = 9 by noticing that x must be a number whose square is 9. Thus, or This can be generalized as the square root property. Slide 11.1-8

  8. CLASSROOM EXAMPLE 2 Solving Quadratic Equations of the Form x2 = k Solution: Solve each equation. Write radicals in simplified form. Slide 11.1-9

  9. An expert marksman can hold a silver dollar at forehead level, drop it, draw his gun, and shoot the coin as it passes waist level. If the coin falls about 4 ft, use the formula d = 16t2 to find the time that elapses between the dropping of the coin and the shot. CLASSROOM EXAMPLE 3 Using the Square Root Property in an Application Solution: d = 16t2 4= 16t2 Since time cannot be negative, we discard the negative solution. Therefore, 0.5 sec elapses between the dropping of the coin and the shot. By the square root property, Slide 9.1- 9

  10. Objective 3 Solve equations of the form (ax + b)2 = k, where k >0. Slide 11.1-11

  11. Solve equations of the form (ax + b)2 = k, where k> 0. In each equation in Example 2, the exponent 2 appeared with a single variable as its base. We can extend the square root property to solve equations in which the base is a binomial. Slide 11.1-12

  12. CLASSROOM EXAMPLE 4 Solving Quadratic Equations of the Form (x + b)2 = k Solution: Solve (p– 4)2 = 3. Slide 11.1-13

  13. CLASSROOM EXAMPLE 5 Solving a Quadratic Equation of the Form (ax + b)2 = k Solution: Solve (5m + 1)2 = 7. Slide 11.1-14

  14. Solve quadratic equations with solutions that are not real numbers. Objective 4 Slide 11.1- 14

  15. Solve the equation. The solution set is CLASSROOM EXAMPLE 6 Solve for Nonreal Complex Solutions Solution: Slide 11.1- 15

  16. The solution set is CLASSROOM EXAMPLE 6 Solve for Nonreal Complex Solutions (cont’d) Solve the equation. Solution: Slide 11.1- 16

  17. The solution set is CLASSROOM EXAMPLE 6 Solve for Nonreal Complex Solutions (cont’d) Solve the equation. Solution: Slide 11.1- 17

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