# How do you find the roots, real and imaginary, of y=10x^2 + 9x-1  using the quadratic formula?

Jan 15, 2017

${x}_{1 , 2} = \frac{- B \pm \sqrt{{B}^{2} - 4 A C}}{2 A}$

#### Explanation:

${x}_{1 , 2} = \frac{- 9 \pm \sqrt{{\left(- 9\right)}^{2} - 4 \cdot 10 \cdot \left(- 1\right)}}{2 \cdot 10}$

${x}_{1 , 2} = \frac{- 9 \pm \sqrt{81 + 40}}{20}$

${x}_{1 , 2} = - \frac{9}{20} \pm \frac{1}{20} \sqrt{121} = - \frac{9}{20} \pm \frac{11}{20}$

$\to {x}_{1} = - \frac{9}{20} + \frac{11}{20} = \frac{2}{20} = \frac{1}{10}$

$\to {x}_{2} = - \frac{9}{20} - \frac{11}{20} = - \frac{20}{20} = - 1$