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1. Introduction. In this unit we explain what is meant by a cubic equation and how such an equation can be solved. The general strategy for solving a cubic equation is to reduce it to a quadratic equation, and then solve the quadratic by the usual means, either by factorising or using the formula. 2. Cubic equations and the nature of their roots.
Part 1 presents mathematical formulas together with other material, such as definitions, theorems, graphs, diagrams, etc., essential for proper understanding and application of the formulas.
The cubic formula for solving cubic polynomials is seldom used, even though it has been known since the 1545 when Girolamo Cardano published his Ars Magna [2]. This cubic formula, like the quadratic formula, gives the exact answer in closed form.
A Simplification for cubics. The cubic formula tells us the roots of polynomials of the form ax3 + bx2 + cx + d. Equivalently, the cubic formula tells us the solutions of equations of the form ax3 + bx2 + cx + d = 0.
A cubic is a polynomial which has an x 3 term as the highest power of x. Some cubic graphs have two turning points – a minimum point and a maximum point. A cubic graph with two turning points can touch or cross the x axis between one and three times.
A cubic curve C has equation y x x x= + − +3 2 24 36 . a) Find the values of the constants A and B, so that x x x x x Bx C3 2 2+ − + ≡ + + +24 36 6( )( ), and hence express y as a product of three linear factors. b) Sketch the graph of C. The sketch must include any points where the graph meets the coordinate axes.
Cubes. To cube a number we multiply the number by itself, and then multiply that answer by the number again. We can write cubed using a small (superscript) 3. 2³ means 2 cubed. 3³ means 3 cubed. Example 3: Work out the value of 4³. To work out the value of 4 cubed we need to calculate 4 × 4 × 4. 4 × 4 = 16.
