Find roots of polynomial $$ p(x) = 3x^2+2x^2-19+6 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= \frac{\sqrt{ 65 }}{ 5 }\\[1 em]x_2 &= - \frac{\sqrt{ 65 }}{ 5 } \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ \color{blue}{3x^2} + \color{blue}{2x^2} \color{red}{-19} + \color{red}{6} = \color{blue}{5x^2} \color{red}{-13} $$Step 2:
The solutions of $ 5x^2-13 = 0 $ are: $ x = - \dfrac{\sqrt{ 65 }}{ 5 } ~ \text{and} ~ x = \dfrac{\sqrt{ 65 }}{ 5 }$.
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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