Question
Find roots of polynomial $$ p(x) = 25-12t+\frac{2}{5}t^2 $$
Answer
The roots of polynomial $ p(t) $ are:
$$ \begin{aligned}t_1 &= 27.7475\\[1 em]t_2 &= 2.2525 \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 5 } $.
$$ \begin{aligned} 25-12t+\frac{2}{5}t^2 & = 0 ~~~ / \cdot \color{blue}{ 5 } \\[1 em] 125-60t+2t^2 & = 0 \end{aligned} $$Step 2:
Write polynomial in descending order
$$ \begin{aligned} 125-60t+2t^2 & = 0\\[1 em] 2t^2-60t+125 & = 0 \end{aligned} $$Step 3:
The solutions of $ 2t^2-60t+125 = 0 $ are: $ t = 15-\dfrac{ 5 \sqrt{ 26}}{ 2 } ~ \text{and} ~ t = 15+\dfrac{ 5 \sqrt{ 26}}{ 2 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.
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