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