The Quadratic Formula..

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Presentation transcript:

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 : ax2 + bx + c = 0 The roots of the quadratic equation are given by :

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.

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.

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.

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.

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:

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

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

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

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