Find roots of polynomial $$ p(x) = x^2-4x-8x-\frac{3}{2}-9 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 12.8191\\[1 em]x_2 &= -0.8191 \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 2 } $.
$$ \begin{aligned} x^2-4x-8x-\frac{3}{2}-9 & = 0 ~~~ / \cdot \color{blue}{ 2 } \\[1 em] 2x^2-8x-16x-3-18 & = 0 \end{aligned} $$Step 2:
Combine like terms:
$$ 2x^2 \color{blue}{-8x} \color{blue}{-16x} \color{red}{-3} \color{red}{-18} = 2x^2 \color{blue}{-24x} \color{red}{-21} $$Step 3:
The solutions of $ 2x^2-24x-21 = 0 $ are: $ x = 6-\dfrac{\sqrt{ 186 }}{ 2 } ~ \text{and} ~ x = 6+\dfrac{\sqrt{ 186 }}{ 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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