Quadratic formula

Uses of the quadratic formula

The main use is for solving the roots of a quadratic equation (finding the values of where )

It also has another use - the discriminant (the part under the square root) can tell us a lot, for example, the number of roots the equation has. See the page on the discriminant for more information.

Finding the roots

To find the roots of a quadratic equation using the quadratic formula, we substitute the coefficients of the equation into the quadratic formula.

The equation should be in the form , so just substitute those values into the formula above.

Remember to find both the positive and negative square roots of the discriminant () to get both roots! You can do this on your calculator by calculating and separately.

Example questions

Find the roots of

• Substitute into the quadratic formula:
• Calculate both roots:
• Answer: and

Find the roots of

• Substitute into the quadratic formula:
• Calculate both roots:
• Answer: and

Find the roots of

• Substitute into the quadratic formula:
• Calculate both roots:
• Answer: and