Mathematics (AS)·Equations, expressions, identities and inequalities · NSSCAS 1.1.3
Identities, unknown coefficients & disguised quadratics
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Ever wondered why some maths statements use a triple bar instead of an equals sign? In this lesson you'll learn the real difference between identities and equations, and use identities to find unknown coefficients two clever ways. Then we unmask disguised quadratics — quartics and square-root equations with a friendly quadratic hiding inside. Finally, you'll rebuild the equation of a quadratic or cubic graph from its roots and a point. Real exam gold, taught slowly.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 1.1.3):
- Interpret the difference between identities (≡, true for all x) and equations (true for some x)
- Use identities to determine unknown coefficients in polynomials, by comparing coefficients and by substituting convenient values of x
- Recognise and solve equations in x which are quadratic in some function of x, such as x⁴ − 5x² + 4 = 0 and x − 5√x + 6 = 0
- Find the equation of a quadratic or cubic graph given sufficient information, such as its roots and one point, or its vertex and a point
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