The function $\mathrm{f}(x)=2{{x}^{3}}+a{{x}^{2}}-bx-6$ has factors $(x-2)$ and \(\mathrm{(}x+3)

Question

The function $\mathrm{f}(x)=2{{x}^{3}}+a{{x}^{2}}-bx-6$ has factors $(x-2)$ and $\mathrm{(}x+3)$. Find the value of $a$ and $b$. Factorise $2{{x}^{3}}+a{{x}^{2}}-bx-6$ completely. Hence, solve $2{{(x+1)}^{3}}+3{{(x+1)}^{2}}-11x-17=0$.

Accepted Answer

(a) $a=3,\ b=11$ (b) $(2x+1)(x-2)(x+3)$ (c) $x=1,\ -\frac{3}{2},\ -4$

Polynomials, Cubic Equations and Partial Fractions - Cubic Expressions and Equations

Polynomials, Cubic Equations and Partial Fractions - Cubic Expressions and Equations

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