Find roots of polynomial $$ p(x) = 11664-4374x+567x^2 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= \frac{ 27 }{ 7 }+\frac{ 3 \sqrt{ 31}}{ 7 }i\\[1 em]x_2 &= \frac{ 27 }{ 7 }-3 \frac{\sqrt{ 31 }}{ 7 }i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 11664-4374x+567x^2 & = 0\\[1 em] 567x^2-4374x+11664 & = 0 \end{aligned} $$Step 2:
The solutions of $ 567x^2-4374x+11664 = 0 $ are: $ x = \dfrac{ 27 }{ 7 }+\dfrac{ 3 \sqrt{ 31}}{ 7 }i ~ \text{and} ~ x = \dfrac{ 27 }{ 7 }-\dfrac{ 3 \sqrt{ 31}}{ 7 }i$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.
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