Find roots of polynomial $$ p(x) = x^2-6x-27-x-9 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 10.4462\\[1 em]x_2 &= -3.4462 \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^2 \color{blue}{-6x} \color{red}{-27} \color{blue}{-x} \color{red}{-9} = x^2 \color{blue}{-7x} \color{red}{-36} $$Step 2:
The solutions of $ x^2-7x-36 = 0 $ are: $ x = \dfrac{ 7 }{ 2 }-\dfrac{\sqrt{ 193 }}{ 2 } ~ \text{and} ~ x = \dfrac{ 7 }{ 2 }+\dfrac{\sqrt{ 193 }}{ 2 }$.
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