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The Quadratic Formula.

The Quadratic Formula. What Does The Formula Do ?. The Quadratic formula allows you to find the roots of a quadratic equation (if they exist) even if the quadratic equation does not factorise. The formula states that for a quadratic equation of the form :. ax 2 + bx + c = 0.

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The Quadratic Formula.

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  1. The Quadratic Formula.

  2. What Does The Formula Do ? The Quadratic formula allows you to find the roots of a quadratic equation (if they exist) even if the quadratic equation does not factorise. The formula states that for a quadratic equation of the form : ax2 + bx + c = 0 The roots of the quadratic equation are given by :

  3. Example 1 Use the quadratic formula to solve the equation : x 2 + 5x + 6= 0 Solution: x 2 + 5x + 6= 0 a = 1 b = 5 c = 6 x = - 2 or x = - 3 These are the roots of the equation.

  4. Example 2 Use the quadratic formula to solve the equation : 8x 2 + 2x - 3= 0 Solution: 8x 2 + 2x - 3= 0 a = 8 b = 2 c = -3 x = ½ or x = - ¾ These are the roots of the equation.

  5. Example 3 Use the quadratic formula to solve the equation : 8x 2 - 22x + 15= 0 Solution: 8x 2 - 22x + 15= 0 a = 8 b = -22 c = 15 x = 3/2 or x = 5/4 These are the roots of the equation.

  6. Example 4 Use the quadratic formula to solve for x 2x 2 +3x - 7= 0 Solution: 2x 2 + 3x – 7 = 0 a = 2 b = 3 c = - 7 These are the roots of the equation.

  7. The Quadratic Formula • The solutions of a quadratic equation of the form ax2 + bx + c = 0, where a ≠ 0, are given by the following formula:

  8. Two Rational Roots • Solve by using the Quadratic Formula. Solutions are -2 and 14.

  9. One Rational Root • Solve by using the Quadratic Formula. • The solution is .

  10. Irrational Roots • Solve by using the Quadratic Formula. • The exact solutions are and .

  11. Complex Roots • Solve by using the Quadratic Formula. • The exact solutions are and .

  12. Roots and the Discriminant • The Discriminant = b2 – 4ac • The value of the Discriminant can be used to determine the number and type of roots of a quadratic equation.

  13. Discriminant

  14. Describe Roots • Find the value of the discriminant for each quadratic equation. Then describe the number and type of roots for the equation. • A. The discriminant is 0, so there is one rational root. • B. The discriminant is negative, so there are two complex roots.

  15. Describe Roots • Find the value of the discriminant for each quadratic equation. Then describe the number and type of roots for the equation. • C. The discriminant is 44, which is not a perfect square. Therefore there are two irrational roots. D. The discriminant is 289, which is a perfect square. Therefore, there are two rational roots.

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