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