Find roots of polynomial $$ p(x) = \frac{3}{4}-4x-x^2 $$

The roots of polynomial $ p(x) $ are:

$$ \begin{aligned}x_1 &= 0.1794\\[1 em]x_2 &= -4.1794 \end{aligned} $$

Step 1:

Get rid of fractions by multipling equation by $ \color{blue}{ 4 } $.

$$ \begin{aligned} \frac{3}{4}-4x-x^2 & = 0 ~~~ / \cdot \color{blue}{ 4 } \\[1 em] 3-16x-4x^2 & = 0 \end{aligned} $$

Step 2:

Write polynomial in descending order

$$ \begin{aligned} 3-16x-4x^2 & = 0\\[1 em] -4x^2-16x+3 & = 0 \end{aligned} $$

Step 3:

The solutions of $ -4x^2-16x+3 = 0 $ are: $ x = -2-\dfrac{\sqrt{ 19 }}{ 2 } ~ \text{and} ~ x = -2+\dfrac{\sqrt{ 19 }}{ 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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