Question
Find roots of polynomial $$ p(x) = \frac{2}{3}x^2-5x $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0\\[1 em]x_2 &= \dfrac{ 15 }{ 2 } \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 3 } $.
$$ \begin{aligned} \frac{2}{3}x^2-5x & = 0 ~~~ / \cdot \color{blue}{ 3 } \\[1 em] 2x^2-15x & = 0 \end{aligned} $$Step 2:
Factor out $ \color{blue}{ x }$ from $ 2x^2-15x $ and solve two separate equations:
$$ \begin{aligned} 2x^2-15x & = 0\\[1 em] \color{blue}{ x }\cdot ( 2x-15 ) & = 0 \\[1 em] \color{blue}{ x = 0} ~~ \text{or} ~~ 2x-15 & = 0 \end{aligned} $$One solution is $ \color{blue}{ x = 0 } $. Use second equation to find the remaining roots.
Step 3:
To find the second zero, solve equation $ 2x-15 = 0 $
$$ \begin{aligned} 2x-15 & = 0 \\[1 em] 2 \cdot x & = 15 \\[1 em] x & = \frac{ 15 }{ 2 } \end{aligned} $$This page was created using
Polynomial Roots Calculator