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Pure · SS1–SS2

Polynomials & quadratic roots

Polynomials and the roots of quadratic equations: sums and products of roots, and forming equations.

Before this
Quadratics & their graphsPolynomials & algebraic division
Leads to
Partial fractions

Learn

  1. 1Dividing, factorising and finding unknownsThe General Maths remainder and factor theorems, pushed further: synthetic division, factorising a cubic completely, a factor and a remainder together, dividing by a quadratic, and a quadratic from three of its values.Done20 min
  2. 2The roots α and βUse the sum and product of the roots without solving: expressions such as α² + β², α − β and α³ + β³, and a new equation whose roots are built from α and β.Done18 min
  3. 3Completing the square, the discriminant and inequalitiesWrite ax² + bx + c as p(x + q)² + r, solve quadratic inequalities with any sign in front, and find the range of k that gives real roots.Done20 min

Flashcards

13 cards: the rules, facts and methods to know by heart, with the diagrams from the lessons. They come back until you know them.

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Practise

Answer polynomials & quadratic roots questions one at a time. You'll know straight away whether you're right, with hints and the working step by step.

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Past questions (50)

From 2008–2023: 45 WAEC, 5 NECO. Theory questions first, then objective, newest first.

Theory (36)

Objective (14)