# How do you find the roots, real and imaginary, of y=x^2 + -3x + 14  using the quadratic formula?

May 26, 2018

${x}_{1} = \frac{3}{2} + \frac{\sqrt{47}}{2} i$ or ${x}_{2} = \frac{3}{2} - \frac{\sqrt{47}}{2} i$

#### Explanation:

Using the formula
${x}_{1 , 2} = - \frac{b}{2 a} \setminus \pm \frac{1}{2 a} \sqrt{{b}^{2} - 4 a c}$
we get
${x}_{1 , 2} = \frac{3}{2} \pm \sqrt{\frac{9}{4} - \frac{56}{4}}$
this gives
${x}_{1 , 2} = \frac{3}{2} \setminus \pm \setminus \frac{\sqrt{47}}{2} i$