Solving Cubic Equations (Grade 12 NSC Matric Mathematics): Quizzes

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Solving Cubic Equations
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What is the general form of a cubic equation?

ax3+bx2+cx+d=0ax^3 + bx^2 + cx + d = 0

Why must the coefficient aa not equal zero in ax3+bx2+cx+d=0ax^3 + bx^2 + cx + d = 0?

Equation would reduce to quadratic or lower

If f(a)=0f(a) = 0 when testing a value, what does this tell us?

(x−a)(x - a) is a factor of the polynomial

What is the first step in solving a cubic equation?

Use factor theorem to find one factor

What is the maximum number of real solutions a cubic equation can have?

3

Which values should you test first when using the factor theorem?

Simple integers like pm1,pm2,pm3pm 1, pm 2, pm 3

For f(x)=6x3−5x2−17x+6f(x) = 6x^3 - 5x^2 - 17x + 6, what is f(2)f(2)?

0

When should you use the quadratic formula in solving cubic equations?

When quadratic factor can't be factorised

If b2−4ac<0b^2 - 4ac < 0 for the quadratic factor, what does this mean?

Cubic has only one real solution

After finding (x+2)(x+2) as a factor of x3−2x2−6x+4x^3 - 2x^2 - 6x + 4, what is the quadratic factor?

x2−4x+2x^2 - 4x + 2

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