Find roots of polynomial $$ p(x) = -2x^2+2x+\frac{1}{4} $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.1124\\[1 em]x_2 &= -0.1124 \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 4 } $.
$$ \begin{aligned} -2x^2+2x+\frac{1}{4} & = 0 ~~~ / \cdot \color{blue}{ 4 } \\[1 em] -8x^2+8x+1 & = 0 \end{aligned} $$Step 2:
The solutions of $ -8x^2+8x+1 = 0 $ are: $ x = \dfrac{ 1 }{ 2 }-\dfrac{\sqrt{ 6 }}{ 4 } ~ \text{and} ~ x = \dfrac{ 1 }{ 2 }+\dfrac{\sqrt{ 6 }}{ 4 }$.
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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