Quadratic equation

How it is used

Solved by factorising, completing the square or the quadratic formula, x = (−b ± √(b² − 4ac)) / 2a. The discriminant, b² − 4ac, tells you whether there are two, one or no real roots. People often just say 'a quadratic'.

Example sentences

1. This quadratic equation doesn't factorise nicely, so use the formula.

2. The discriminant is negative, so the quadratic equation has no real roots.

Common collocations

• solve a quadratic equation
• quadratic formula
• complete the square
• roots of a quadratic

Related terms

• equationA mathematical statement with an equals sign, showing that two expressions have the same value, such as 2x + 3 = 11.
• rootA value of the variable that makes an equation or polynomial equal to zero; the roots of x² − 5x + 6 = 0 are 2 and 3.
• polynomialAn expression made of terms with whole-number powers of a variable, added or subtracted, such as 3x⁴ − 2x² + x − 7.
• factorA number or expression that divides another exactly, with no remainder; the factors of 12 are 1, 2, 3, 4, 6 and 12.
• coefficientThe number that multiplies a variable in a term; in 5x² − 3x, the coefficient of x² is 5 and the coefficient of x is −3.

More terms: Algebra and Equations

• variable
• solve
• simplify
• expression
• inequality
• plug in
• cancel out