Quadratic equations · Year 11

In Year 11 you learn: the quadratic formula.

A quadratic equation has an x² term, like x² + 5x + 6 = 0, and usually has two solutions. You can solve it by factorising, by completing the square, or with the quadratic formula, which always works.

Key facts

• Rearrange so that one side is 0 before you solve.
• If two brackets multiply to 0, one of them must be 0: (x − 2)(x + 5) = 0 gives x = 2 or x = −5.
• Quadratic formula for ax² + bx + c = 0: x = (−b ± √(b² − 4ac))/(2a).
• The discriminant b² − 4ac: positive → two solutions; zero → one repeated solution; negative → no real solutions.
• x² = 25 has two solutions, x = 5 and x = −5.
• The solutions are where the graph of y = ax² + bx + c crosses the x-axis.

Worked examples

Other years

• Quadratic equations · Year 10
• Quadratic equations · Year 12