Paper 1 · Algebra
⏱ Tested in 2 exam questions since 2017
Lesson 12 of 23
Algebra 12 – Nature of cubic roots
In this lesson you’ll learn to
- Tell apart the three root scenarios: 3 distinct, 3 with 2 equal, 1 real + 2 imaginary
- Prove a cubic has only one real root by finding it, then testing b² − 4ac
- Reduce a cubic to its quotient quadratic via trial and error + long division
Formula used
Roots of the quadratic equation
x = (-b ± √(b² − 4ac)) / 2a
On page 20 of the log tables — read it off, don’t memorise.Most recent exam questions
- 2025 Paper 1 Q1(c) — factor theorem + polynomial long division + quadratic factoring
- 2017 Paper 1 Q5(c) — vertical translation of a cubic + counting real roots from the graph. The cubic f(x) (fr…
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