Question
Find roots of polynomial $$ p(x) = -\frac{6}{5}x^2+\frac{26}{5}-\frac{24}{5} $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= \dfrac{\sqrt{ 3 }}{ 3 }\\[1 em]x_2 &= - \dfrac{\sqrt{ 3 }}{ 3 } \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 5 } $.
$$ \begin{aligned} -\frac{6}{5}x^2+\frac{26}{5}-\frac{24}{5} & = 0 ~~~ / \cdot \color{blue}{ 5 } \\[1 em] -6x^2+26-24 & = 0 \end{aligned} $$Step 2:
Combine like terms:
$$ -6x^2+ \color{blue}{26} \color{blue}{-24} = -6x^2+ \color{blue}{2} $$Step 3:
The solutions of $ -6x^2+2 = 0 $ are: $ x = - \dfrac{\sqrt{ 3 }}{ 3 } ~ \text{and} ~ x = \dfrac{\sqrt{ 3 }}{ 3 }$.
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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