quadratic formula

The quadratic formula solves any equation written as ax² + bx + c = 0, where a is not zero. Read the three coefficients first — a is the number on x², b is the number on x, and c is the constant — then substitute: x = (−b ± √(b² − 4ac)) ÷ (2a). The part under the root, b² − 4ac, is called the discriminant; a positive value gives two real solutions, zero gives one, and a negative value gives none among the real numbers. For x² − 5x + 6 = 0, a = 1, b = −5 and c = 6, so b² − 4ac = 25 − 24 = 1, the square root of 1 is 1, and x = (5 ± 1) ÷ 2 = 3 or 2. The two common errors are a sign slip on b — the formula uses −b — and dropping the ±, which reports one solution where there are two.