Using the quadratic formula
The quadratic equation of the following form can be solved using the second solution:
ax² + bx + c = 0
For example, when using the above formula to solve 2x² + 5x – 1 = 0, the following steps are taken:
2x² + 5x – 1 = 0 (insert into the above formula format
Using the b² – 4ac formula further
Fort the above formula, the b² – 4ac can be used to recognise how many solution there can be:
- If b² – 4ac = positive – there are two solutions.
- If b² – 4ac = 0 – there is one solution.
- If b² – 4ac = negative – there are no solutions.
This can be graphically demonstrated using the following graphs: