Lesson 1 of 1
SHORTCUT
When factorising fails, the formula never does.
The question
Solve x² − 5x + 6 = 0
x = (−b ± √(b² − 4ac)) ÷ 2a. Identify a, b and c first, then substitute carefully.
So: x = 2 or x = 3
Sing it: 'x equals minus b, plus or minus the square root, of b squared minus four a c, all over two a.' The tune is what survives exam nerves.
Work out the discriminant b² − 4ac on its own line first. It tells you immediately how many roots there are — positive means two, zero means one repeated, negative means none — and questions often ask only for that.
The formula is what you get by completing the square on the general equation ax² + bx + c = 0. It is that one piece of working, done once, for every quadratic there will ever be.
Discriminant of x² + 4x + 4 (number only)
How many real roots does x² + x + 5 have?
Smaller root of x² − 7x + 12 = 0
