Question
Find roots of polynomial $$ p(x) = 1-\frac{3}{4}z-\frac{1}{8}z^2 $$
Answer
The roots of polynomial $ p(z) $ are:
$$ \begin{aligned}z_1 &= 1.1231\\[1 em]z_2 &= -7.1231 \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 8 } $.
$$ \begin{aligned} 1-\frac{3}{4}z-\frac{1}{8}z^2 & = 0 ~~~ / \cdot \color{blue}{ 8 } \\[1 em] 8-6z-z^2 & = 0 \end{aligned} $$Step 2:
Write polynomial in descending order
$$ \begin{aligned} 8-6z-z^2 & = 0\\[1 em] -z^2-6z+8 & = 0 \end{aligned} $$Step 3:
The solutions of $ -z^2-6z+8 = 0 $ are: $ z = -3-\sqrt{ 17 } ~ \text{and} ~ z = -3+\sqrt{ 17 }$.
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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