Quadratic Equations

A quadratic equation has the form ax2 + bx + c = 0 where a ≠ 0. In this topic you will learn to solve quadratics by factorising, completing the square, and using the quadratic formula. You will also learn how to use the discriminant to check the type of roots.

  • Solving by factorisation
  • Completing the square
  • Quadratic formula and discriminant
  • Problems leading to quadratics

Lessons for Quadratic Equations

Solving by Factorisation

Method1. Write in form ax2 + bx + c = 02. Factorise the left side3. If AB = 0 then …

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Completing the Square

Method for x2 + bx + c = 01. Take half the coefficient of x, square it.2. x2 + bx …

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Quadratic Formula and the Discriminant

Quadratic FormulaFor ax2 + bx + c = 0,x = [-b ± √(b2 - 4ac)] / 2aThis works for all …

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Problems Leading to Quadratic Equations

Word problemsMany problems give two unknowns but only one equation if you substitute. Common types:1. Consecutive numbers: x and x+12. …

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Exercises for Quadratic Equations

Solve by factorising

Solve by factorisation:x2 - 7x + 12 = 0x2 + x - 20 = 0x2 - 9 = 02x2 + …

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Solve by completing the square

Solve by completing the square. Leave surds in your answer if needed:x2 + 4x - 5 = 0x2 - 6x …

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Use the formula and find the discriminant

1. Solve using the formula: x2 - 4x + 1 = 0. Give answers to 2 d.p.2. Solve: 3x2 + …

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Form and solve quadratics

Form an equation and solve:The product of two consecutive even numbers is 168. Find the numbers.A rectangle has length 3 …

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