Question
Find roots of polynomial $$ p(x) = -x^2-\frac{3}{2}x-19 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -\dfrac{ 3 }{ 4 }+\dfrac{\sqrt{ 295 }}{ 4 }i\\[1 em]x_2 &= -\dfrac{ 3 }{ 4 }- \dfrac{\sqrt{ 295 }}{ 4 }i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 2 } $.
$$ \begin{aligned} -x^2-\frac{3}{2}x-19 & = 0 ~~~ / \cdot \color{blue}{ 2 } \\[1 em] -2x^2-3x-38 & = 0 \end{aligned} $$Step 2:
The solutions of $ -2x^2-3x-38 = 0 $ are: $ x = -\dfrac{ 3 }{ 4 }+\dfrac{\sqrt{ 295 }}{ 4 }i ~ \text{and} ~ x = -\dfrac{ 3 }{ 4 }-\dfrac{\sqrt{ 295 }}{ 4 }i$.
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