How do you solve the polynomial 10x^3-5x^2=0?

Nov 18, 2014

In order to solve the algebraic equation for the variable x we would begin by factoring out the common factor from the equation
$10 {x}^{3} - 5 {x}^{2} = 0$
The common factor between $10 {x}^{3}$ and $5 {x}^{2}$ is $5 {x}^{2}$

$5 {x}^{2} \left(2 x - 1\right) = 0$

Next we would set each value of x equal to 0

$5 {x}^{2} = 0 \mathmr{and} \left(2 x - 1\right) = 0$

$5 {x}^{2} = 0$ divide by 5 and square root each side
${x}^{2} = \frac{0}{5}$
$x = 0$

$\left(2 x - 1\right) = 0$ add 1 and divide by 2 on each side
$2 x = 0 + 1$
$x = \frac{1}{2}$

$x = \left\{0 , \frac{1}{2}\right\}$