Question
Find roots of polynomial $$ p(x) = 2x^5-9x^4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0\\[1 em]x_2 &= \dfrac{ 9 }{ 2 } \end{aligned} $$Explanation
Step 1:
Factor out $ \color{blue}{ x^4 }$ from $ 2x^5-9x^4 $ and solve two separate equations:
$$ \begin{aligned} 2x^5-9x^4 & = 0\\[1 em] \color{blue}{ x^4 }\cdot ( 2x-9 ) & = 0 \\[1 em] \color{blue}{ x^4 = 0} ~~ \text{or} ~~ 2x-9 & = 0 \end{aligned} $$One solution is $ \color{blue}{ x = 0 } $. Use second equation to find the remaining roots.
Step 2:
To find the last zero, solve equation $ 2x-9 = 0 $
$$ \begin{aligned} 2x-9 & = 0 \\[1 em] 2 \cdot x & = 9 \\[1 em] x & = \frac{ 9 }{ 2 } \end{aligned} $$This page was created using
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