Find roots of polynomial $$ p(x) = 3x-\frac{1}{2}x^2-5 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 3+i\\[1 em]x_2 &= 3-i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 2 } $.
$$ \begin{aligned} 3x-\frac{1}{2}x^2-5 & = 0 ~~~ / \cdot \color{blue}{ 2 } \\[1 em] 6x-x^2-10 & = 0 \end{aligned} $$Step 2:
Write polynomial in descending order
$$ \begin{aligned} 6x-x^2-10 & = 0\\[1 em] -x^2+6x-10 & = 0 \end{aligned} $$Step 3:
The solutions of $ -x^2+6x-10 = 0 $ are: $ x = 3+i ~ \text{and} ~ x = 3-i$.
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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