Find roots of polynomial $$ p(x) = x^2-8x^2+22x-20 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= \frac{ 11 }{ 7 }+\frac{\sqrt{ 19 }}{ 7 }i\\[1 em]x_2 &= \frac{ 11 }{ 7 }- \frac{\sqrt{ 19 }}{ 7 }i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ \color{blue}{x^2} \color{blue}{-8x^2} +22x-20 = \color{blue}{-7x^2} +22x-20 $$Step 2:
The solutions of $ -7x^2+22x-20 = 0 $ are: $ x = \dfrac{ 11 }{ 7 }+\dfrac{\sqrt{ 19 }}{ 7 }i ~ \text{and} ~ x = \dfrac{ 11 }{ 7 }-\dfrac{\sqrt{ 19 }}{ 7 }i$.
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