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Objective The student will be able to:

Objective The student will be able to:. use the zero product property to solve equations SOL: A.14. Designed by Skip Tyler, Varina High School. Zero Product Property. If a • b = 0 then a=0, b=0, or both a and b equal 0. 1. Solve (x + 7)(x - 4) = 0.

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Objective The student will be able to:

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  1. ObjectiveThe student will be able to: use the zero product property to solve equations SOL: A.14 Designed by Skip Tyler, Varina High School

  2. Zero Product Property If a • b = 0 then a=0, b=0, or both a and b equal 0.

  3. 1. Solve (x + 7)(x - 4) = 0 Using the Zero Product Property, you know that either x + 7 = 0or x - 4 = 0 Solve each equation. x = -7 or x = 4 {-7, 4}

  4. 2. Solve (3y - 5)(y - 2) = 0 3y - 5 = 0 or y - 2 = 0 3y = 5 or y = 2 y = 5/3 or y = 2 {5/3, 2}

  5. 3. Solve (x + 5)(2x - 6) = 0 x + 5 = 0 or 2x - 6 = 0 x = -5 or 2x = 6 x = -5 or x = 3 {-5, 3}

  6. 4. Solve (6x + 9)(4x - 11) = 0 • {-3/2, 11/4} • {-3/2, 3} • {3/2, -11/4} • {3/2, -3}

  7. 4 steps for solving a quadratic equation Set = 0 Factor Split Solve/Check • Set the equation equal to 0. • Factor the equation. • Set each part equal to 0 • Solve for the variable - Check each answer on your calculator!

  8. 5. Solve x2 - 11x = 0 Set = 0 Factor GCF Check GCF = x x(x - 11) = 0 x = 0 or x - 11 = 0 x = 0 or x = 11 {0, 11}

  9. 6. Solve. -24a +144 = -a2 Set = 0 Factor Trinomial Check Put it in descending order. a2 - 24a + 144 = 0 (a – 12)(a – 12) = 0 (a - 12)2 = 0 a - 12 = 0 a = 12 {12}

  10. 7. Solve 4m2 + 25 = 20m 4m2 - 20m + 25 = 0 (2m - 5)(2m - 5) = 0 2m - 5 = 0 2m = 5 m = Set = 0 Factor Perfect Squares! CHECK with FOIL

  11. Set = 0 Factor GCF, then Trinomial 8. Solve x3 + 2x2 = 15x x3 + 2x2 - 15x = 0 x(x2 + 2x - 15) = 0 x(x + 5)(x - 3) = 0 x = 0or x + 5 = 0or x - 3 = 0 {0, -5, 3}

  12. 9. Solve a2 – 3a = 40 • {-8, 5} • {-5, 8} • {-8, -5} • {5, 8}

  13. 10. Solve 4r3 – 16r = 0 • {-16, 4} • {-4, 16} • {0, 2} • {0, 4} • {-2, 0, 2} The degree will tell you how many answers you have!

  14. Maria told this puzzle to her friends. “The product of four times my age and 45 less than three times my age is zero. How old am I?” Find Maria’s age. Let m = Maria’s age. 4m(3m - 45) = 0 4m = 0 or 3m - 45 = 0 m = 0 or 3m = 45 m = 0 or m = 15 0 is not reasonable so Maria is 15 years old!!

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