Question
Find roots of polynomial $$ p(x) = x^2-\frac{3}{4}x+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= \dfrac{ 3 }{ 8 }+\dfrac{\sqrt{ 55 }}{ 8 }i\\[1 em]x_2 &= \dfrac{ 3 }{ 8 }- \dfrac{\sqrt{ 55 }}{ 8 }i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 4 } $.
$$ \begin{aligned} x^2-\frac{3}{4}x+1 & = 0 ~~~ / \cdot \color{blue}{ 4 } \\[1 em] 4x^2-3x+4 & = 0 \end{aligned} $$Step 2:
The solutions of $ 4x^2-3x+4 = 0 $ are: $ x = \dfrac{ 3 }{ 8 }+\dfrac{\sqrt{ 55 }}{ 8 }i ~ \text{and} ~ x = \dfrac{ 3 }{ 8 }-\dfrac{\sqrt{ 55 }}{ 8 }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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