Question
Find roots of polynomial $$ p(x) = 20t-16t^2 $$
Answer
The roots of polynomial $ p(t) $ are:
$$ \begin{aligned}t_1 &= 0\\[1 em]t_2 &= \dfrac{ 5 }{ 4 } \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 20t-16t^2 & = 0\\[1 em] -16t^2+20t & = 0 \end{aligned} $$Step 2:
Factor out $ \color{blue}{ -4t }$ from $ -16t^2+20t $ and solve two separate equations:
$$ \begin{aligned} -16t^2+20t & = 0\\[1 em] \color{blue}{ -4t }\cdot ( 4t-5 ) & = 0 \\[1 em] \color{blue}{ -4t = 0} ~~ \text{or} ~~ 4t-5 & = 0 \end{aligned} $$One solution is $ \color{blue}{ t = 0 } $. Use second equation to find the remaining roots.
Step 3:
To find the second zero, solve equation $ 4t-5 = 0 $
$$ \begin{aligned} 4t-5 & = 0 \\[1 em] 4 \cdot t & = 5 \\[1 em] t & = \frac{ 5 }{ 4 } \end{aligned} $$This page was created using
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