Find roots of polynomial $$ p(x) = 60+5l+2l^2 $$
Answer
The roots of polynomial $ p(l) $ are:
$$ \begin{aligned}l_1 &= -\frac{ 5 }{ 4 }+\frac{\sqrt{ 455 }}{ 4 }i\\[1 em]l_2 &= -\frac{ 5 }{ 4 }- \frac{\sqrt{ 455 }}{ 4 }i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 60+5l+2l^2 & = 0\\[1 em] 2l^2+5l+60 & = 0 \end{aligned} $$Step 2:
The solutions of $ 2l^2+5l+60 = 0 $ are: $ l = -\dfrac{ 5 }{ 4 }+\dfrac{\sqrt{ 455 }}{ 4 }i ~ \text{and} ~ l = -\dfrac{ 5 }{ 4 }-\dfrac{\sqrt{ 455 }}{ 4 }i$.
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