Question

List the roots of f(x) = 24x^3 – 10x2 -7x + 2.

Answer 1

\[\begin{array}{l} \begin{array}{l} \text{Solve for }x\text{ over the real numbers}: \\ 24 x^3-10 x^2-7 x+2=0 \\\end{array} \\\hline \fbox{$\begin{array}{l} \\ \text{The left hand side factors into a product with three terms}: \\ (2 x+1) (3 x-2) (4 x-1)=0 \\\end{array}$} \\ \fbox{$\begin{array}{l} \\ \text{Split into }\text{three}\text{ equations}: \\ 2 x+1=0\text{ or }3 x-2=0\text{ or }4 x-1=0 \\\end{array}$} \\ \fbox{$\begin{array}{l} \\ \text{Subtract }1\text{ from both sides}: \\ \begin{array}{c} 2 x=-1 \\\end{array}\text{ or }3 x-2=0\text{ or }4 x-1=0 \\\end{array}$} \\ \fbox{$\begin{array}{l} \\ \text{Divide both sides by }2: \\ \begin{array}{c} x=-\frac{1}{2} \\\end{array}\text{ or }3 x-2=0\text{ or }4 x-1=0 \\\end{array}$} \\ \fbox{$\begin{array}{l} \\ \text{Add }2\text{ to both sides}: \\ x=-\frac{1}{2}\text{ or }\begin{array}{c} 3 x=2 \\\end{array}\text{ or }4 x-1=0 \\\end{array}$} \\ \fbox{$\begin{array}{l} \\ \text{Divide both sides by }3: \\ x=-\frac{1}{2}\text{ or }\begin{array}{c} x=\frac{2}{3} \\\end{array}\text{ or }4 x-1=0 \\\end{array}$} \\ \fbox{$\begin{array}{l} \\ \text{Add }1\text{ to both sides}: \\ x=-\frac{1}{2}\text{ or }x=\frac{2}{3}\text{ or }\begin{array}{c} 4 x=1 \\\end{array} \\\end{array}$} \\ \fbox{$\begin{array}{l} \\ \text{Divide both sides by }4: \\ \begin{array}{\ll} \text{Answer}: & \\ \text{} & x=-\frac{1}{2}\text{ or }x=\frac{2}{3}\text{ or }\begin{array}{c} x=\frac{1}{4} \\\end{array} \\\end{array} \\\end{array}$} \\\end{array}\]

Answer 2

thank you for ur help