Solving Cubic Equations (VCE SSCE Mathematical Methods): Flashcards

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Solving cubic equations
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Primary strategy for solving cubic equations

Factorise the expression first

Null factor theorem

If product = 0, at least one factor must = 0

Max number of solutions a cubic equation can have

Up to three solutions

What to always check first when factorising cubics

Common factors

Factor theorem states what about P(a)=0P(a) = 0?

(xa)(x - a) is a factor of polynomial P(x)P(x)

Which values to test first using factor theorem?

±1,±2,±3\pm 1, \pm 2, \pm 3

What is grouping method in factorisation?

Group terms in pairs to identify common factors

How many real solutions can a cubic have?

One, two, or three

Negative discriminant means what for quadratic factor?

No real solutions, can't be factorised further

Alternative terms for solutions of equations

Roots or zeros

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