1. 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

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

3. 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.

4. 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.

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

6. 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.

7. 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