Given $\mathrm{f}(x)=2{{x}^{3}}-5{{x}^{2}}-4x+12$ Show that $x=2$ is a root of \(\math

Question

Given $\mathrm{f}(x)=2{{x}^{3}}-5{{x}^{2}}-4x+12$ Show that $x=2$ is a root of $\mathrm{f}(x)=0$, Factorise $\mathrm{f}(x)$ completely, Hence, solve the equation $2{{\left( \frac{1}{v} \right)}^{3}}-5{{\left( \frac{1}{v} \right)}^{2}}=4\left( \frac{1}{v}-3 \right)$.

Accepted Answer

(a) shown; (b) f(x)=(x-2)^2(2x+3); (c) v=1/2 or -2/3.

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

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

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