Question

How do you find the roots, real and imaginary, of `y= x^2 - 8x + 15` using the quadratic formula?

Answer 1

Apply the quadratic formula to find that the roots are `x=3` and `x=5`.

Explanation:

The quadratic formula states that
`ax^2 + bx+c = 0 => x = (-b+-sqrt(b^2-4ac))/(2a)`
Note that the solutions to `x` for the initial equation are the roots of
`f(x) = ax^2 + bx + c`.

Applying that here, we get
`x^2 - 8x + 15 = 0`

`=> x = (-(-8) +- sqrt( (-8)^2-4(15)(1)))/(2(1))`

`= (8+-sqrt(4))/2`

`= 4+-1`

Thus the roots are `x=3` and `x=5`.