Find roots of polynomial $$ p(x) = -\frac{5}{8}x^2+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= \frac{ 2 \sqrt{ 10}}{ 5 }\\[1 em]x_2 &= -2 \frac{\sqrt{ 10 }}{ 5 } \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 8 } $.
$$ \begin{aligned} -\frac{5}{8}x^2+1 & = 0 ~~~ / \cdot \color{blue}{ 8 } \\[1 em] -5x^2+8 & = 0 \end{aligned} $$Step 2:
The solutions of $ -5x^2+8 = 0 $ are: $ x = -2 \dfrac{\sqrt{ 10 }}{ 5 } ~ \text{and} ~ x = \dfrac{ 2 \sqrt{ 10}}{ 5 }$.
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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