Find roots of polynomial $$ p(x) = 2x^2-7x^2+58x-78 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 10.0474\\[1 em]x_2 &= 1.5526 \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ \color{blue}{2x^2} \color{blue}{-7x^2} +58x-78 = \color{blue}{-5x^2} +58x-78 $$Step 2:
The solutions of $ -5x^2+58x-78 = 0 $ are: $ x = \dfrac{ 29 }{ 5 }-\dfrac{\sqrt{ 451 }}{ 5 } ~ \text{and} ~ x = \dfrac{ 29 }{ 5 }+\dfrac{\sqrt{ 451 }}{ 5 }$.
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