Quadratic Equations
Solving quadratics by factorisation and by formula, reading the discriminant, using the sum and product of roots, forming a quadratic from its roots, and the compare-the-roots question.
What you will be able to do
- Solve a quadratic by factorisation and by the quadratic formula.
- Use the discriminant to state the nature of the roots without solving.
- Apply sum of roots = -b/a and product of roots = c/a, and form a quadratic from given roots.
- Answer a compare-the-roots question by finding both root sets and checking the ranges.
What is inside this lesson
- 1Standard form
- 2The quadratic formula
- 3Solving by factorisation
- 4The discriminant and the nature of the roots
- 5Sum and product of the roots
- 6The compare-the-roots question
- 7Worked examples
- 8Common mistakes
- 9Quick revision
- 10Practice
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Standard form
A quadratic equation is one that can be written as ax^2 plus bx plus c equals 0, with a not equal to 0. The letters a, b and c are the coefficients; x is the unknown.
A quadratic has at most two roots. Bank exams ask you to solve one, to state how many real roots it has, to use the sum or product of the roots, or to compare the roots of two quadratics and say how one variable relates to the other. Each of these is a short calculation once you know the four tools below.
This topic writes x^2 for x squared and uses the caret sign for other powers.
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