(a) List the set of possible rational zeros of the polynomial function F(x) = 2x3 - 11x2 + 13x - 4. (b) Find all rational zeros of F(x). Only do part B

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Answer to a math question (a) List the set of possible rational zeros of the polynomial function F(x) = 2x3 - 11x2 + 13x - 4. (b) Find all rational zeros of F(x). Only do part B

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96 Answers

$0=2{x}^{3}-11{x}^{2}+13x-4$

$0-2{x}^{3}+11{x}^{2}-13x+4=0$

$-2{x}^{3}+11{x}^{2}-13x+4=0$

$-2{x}^{3}+2{x}^{2}+9{x}^{2}-13x+4=0$

$-2{x}^{3}+2{x}^{2}+9{x}^{2}-9x-4x+4=0$

$-2{x}^{2} \times \left( x-1 \right)+9{x}^{2}-9x-4x+4=0$

$-2{x}^{2} \times \left( x-1 \right)+9x \times \left( x-1 \right)-4x+4=0$

$-2{x}^{2} \times \left( x-1 \right)+9x \times \left( x-1 \right)-4\left( x-1 \right)=0$

$-\left( x-1 \right) \times \left( 2{x}^{2}-9x+4 \right)=0$

$-\left( x-1 \right) \times \left( 2{x}^{2}-x-8x+4 \right)=0$

$-\left( x-1 \right) \times \left( x \times \left( 2x-1 \right)-8x+4 \right)=0$

$-\left( x-1 \right) \times \left( x \times \left( 2x-1 \right)-4\left( 2x-1 \right) \right)=0$

$-\left( x-1 \right) \times \left( 2x-1 \right) \times \left( x-4 \right)=0$

$\left( x-1 \right) \times \left( 2x-1 \right) \times \left( x-4 \right)=0$

$\begin{array} { l }x-1=0,\\2x-1=0,\\x-4=0\end{array}$

$\begin{array} { l }x=1,\\2x-1=0,\\x-4=0\end{array}$

$\begin{array} { l }x=1,\\x=\frac{ 1 }{ 2 },\\x-4=0\end{array}$

$\begin{array} { l }x=1,\\x=\frac{ 1 }{ 2 },\\x=4\end{array}$

$\begin{align*}&\begin{array} { l }x_1=\frac{ 1 }{ 2 },& x_2=1,& x_3=4\end{array} \\&\begin{array} { l }x_1=0.5,& x_2=1,& x_3=4\end{array}\end{align*}$

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