Question
Find roots of polynomial $$ p(x) = \frac{25}{4}x^2-\frac{9}{4}x-4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1\\[1 em]x_2 &= -\dfrac{ 16 }{ 25 } \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 4 } $.
$$ \begin{aligned} \frac{25}{4}x^2-\frac{9}{4}x-4 & = 0 ~~~ / \cdot \color{blue}{ 4 } \\[1 em] 25x^2-9x-16 & = 0 \end{aligned} $$Step 2:
The solutions of $ 25x^2-9x-16 = 0 $ are: $ x = -\dfrac{ 16 }{ 25 } ~ \text{and} ~ x = 1$.
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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