The Number Under the Root

The expression under the square root in the formula, b^2 - 4ac, has its own name. It is the discriminant. Work it out first, because the rest of the formula depends on it.

For x^2 + 5x + 6 = 0, the discriminant is 5^2 - 4 * 1 * 6 = 1. Its square root is 1, so the formula gives the solutions -2 and -3 with no square root sign left in them.

To work out the discriminant, square b first, then subtract the product 4ac. Keep the signs of all three coefficients. When a coefficient is negative, put it in parentheses before you square or multiply.