Find roots of polynomial $$ p(x) = -\frac{49}{10}x^2+5x+10 $$

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

$$ \begin{aligned}x_1 &= 2.0271\\[1 em]x_2 &= -1.0067 \end{aligned} $$

Step 1:

Get rid of fractions by multipling equation by $ \color{blue}{ 10 } $.

$$ \begin{aligned} -\frac{49}{10}x^2+5x+10 & = 0 ~~~ / \cdot \color{blue}{ 10 } \\[1 em] -49x^2+50x+100 & = 0 \end{aligned} $$

Step 2:

The solutions of $ -49x^2+50x+100 = 0 $ are: $ x = \dfrac{ 25 }{ 49 }-\dfrac{ 5 \sqrt{ 221}}{ 49 } ~ \text{and} ~ x = \dfrac{ 25 }{ 49 }+\dfrac{ 5 \sqrt{ 221}}{ 49 }$.

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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