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 $5^{2}-4\cdot 1\cdot 6 = 1$. 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.