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Maths formula

Quadratic formula:
story, analogy and memory trick

The Quadratic formula is x = (−b ± √(b² − 4ac)) ÷ 2a. It gives the roots of any quadratic equation ax² + bx + c = 0 using only its three coefficients.

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The Quadratic formula

x = (−b ± √(b² − 4ac)) ÷ 2a
  • a, b, ccoefficients in ax² + bx + c = 0
  • xthe roots of the equation
  • b² − 4acthe discriminant, D

The story

A ball is thrown up and a student wants to know when it lands. The height equation is quadratic. Instead of guessing, she puts a, b and c into the formula. The part under the root, b² − 4ac, is the gatekeeper: positive lets in two answers, zero lets in one, negative lets in none.

Real-life analogy

Think of a master key for quadratics. Whatever a, b and c you bring, the formula finds the roots whenever they exist.

Memory trick

Say it like a rhyme: x equals minus b, plus or minus the square root, b squared minus four a c, all over two a.

Exam tip

Check that a is not zero. The discriminant D = b² − 4ac decides the roots: D > 0 gives two real roots, D = 0 gives equal roots, and D < 0 gives no real roots. The sum of the roots is −b/a and the product is c/a.

FAQ

Questions about Quadratic

What is the Quadratic formula?
x = (−b ± √(b² − 4ac)) ÷ 2a. It gives the roots of any quadratic equation ax² + bx + c = 0 using only its three coefficients.
How do I remember the Quadratic formula?
Say it like a rhyme: x equals minus b, plus or minus the square root, b squared minus four a c, all over two a.
What should I watch out for in exams with Quadratic?
Check that a is not zero. The discriminant D = b² − 4ac decides the roots: D > 0 gives two real roots, D = 0 gives equal roots, and D < 0 gives no real roots. The sum of the roots is −b/a and the product is c/a.

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