Find roots of polynomial $$ p(x) = x^2-4x+ \cancel{\frac{17}{4}} -\cancel{1} -\cancel{1}+ \cancel{1}-2 -\cancel{17} $$

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

$$ \begin{aligned}x_1 &= 6.4441\\[1 em]x_2 &= -2.4441 \end{aligned} $$

Step 1:

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

$$ \begin{aligned} x^2-4x+ \cancel{\frac{17}{4}} -\cancel{1} -\cancel{1}+ \cancel{1}-2 -\cancel{17} & = 0 ~~~ / \cdot \color{blue}{ 4 } \\[1 em] 4x^2-16x+17 -\cancel{4} -\cancel{4}+ \cancel{4}-8-68 & = 0 \end{aligned} $$

Step 2:

Combine like terms:

$$ 4x^2-16x+ \color{blue}{17} \, \color{red}{ -\cancel{4}} \, \, \color{orange}{ -\cancel{4}} \,+ \, \color{red}{ \cancel{4}} \, \color{green}{-8} \color{green}{-68} = 4x^2-16x \color{green}{-63} $$

Step 3:

The solutions of $ 4x^2-16x-63 = 0 $ are: $ x = 2-\dfrac{\sqrt{ 79 }}{ 2 } ~ \text{and} ~ x = 2+\dfrac{\sqrt{ 79 }}{ 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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