quadratic formula. If ax2 + bx + c = 0 then

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Presentation transcript:

quadratic formula. If ax2 + bx + c = 0 then When we cannot factorise or solve quadratic equations graphically we need to use the quadratic formula. If ax2 + bx + c = 0 then

Example : Solve x2 + 3x – 3 = 0 ax2 + bx + c = 0 1 3 -3 = 0·79 or – 3·8

These are the roots of the equation. Example 2 Use the quadratic formula to solve the equation : x2 + 5x + 6= 0 ax 2 + bx + c= 0 1 5 6 x = - 2 or x = - 3 These are the roots of the equation.

These are the roots of the equation. Example 3 Use the quadratic formula to solve the equation : 8x2 + 2x - 3= 0 ax 2 + bx + c= 0 8 2 -3 x = 1/2 or x = - 3/4 These are the roots of the equation.

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

These are the roots of the equation. Example 5 Use the quadratic formula to solve the equation : 2x 2 + 3x - 7 = 0 ax 2 + bx + c= 0 2 3 -7 x = 1·27 or x = -2·77 These are the roots of the equation.

x = -1·7, -0·3 x = -3·6, 0·6 x = 1·4, 0·4 x = 1·9, -0·9 Use quadratic formula to solve the following : 2x2 + 4x + 1 = 0 x2 + 3x – 2 = 0 x = -1·7, -0·3 x = -3·6, 0·6 5x2 - 9x + 3 = 0 3x2 - 3x – 5 = 0 x = 1·4, 0·4 x = 1·9, -0·9 4x2 - x - 1 = 0 x2 + 2x - 5 = 0 x = -0·39, 0·64 x = 1·45, -3·45