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

The roots are rational (i.e. real) and are

As it is a complete square one can easily take square root and roots of equation will be rational (i.e. real).

The roots are

By signing up, you agree to our Terms of Service and Privacy Policy

To find the roots of (y = x^2 - x - 2) using the quadratic formula:

- Identify the coefficients: (a = 1), (b = -1), (c = -2).
- Substitute the coefficients into the quadratic formula: (x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}).
- Plug in the values: (x = \frac{{-(-1) \pm \sqrt{{(-1)^2 - 4(1)(-2)}}}}{{2(1)}}).
- Simplify: (x = \frac{{1 \pm \sqrt{{1 + 8}}}}{2}).
- Further simplify: (x = \frac{{1 \pm \sqrt{9}}}{2}).
- Calculate the roots: (x_1 = \frac{{1 + 3}}{2} = 2), (x_2 = \frac{{1 - 3}}{2} = -1).

So, the real roots are (x = 2) and (x = -1), while there are no imaginary roots.

By signing up, you agree to our Terms of Service and Privacy Policy

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7