How do you solve #y=x^3 + 3x^2 - 6x # using the quadratic formula?
This cubic has 3 roots:
We can solve it be dividing through by
This is not a quadratic, it's a cubic, so it'll have 1-3 roots rather than 0-2 (think about the shape of a cubic compared to a parabola-shaped quadratic and how each can cut the x-axis).
It's a tricky one, but we can divide through by x and treat it as:
One root of this will be
The other roots will be when the parenthesis is equal to
And hey presto, we have a quadratic to solve! And we know how to do that: the quadratic formula. For a quadratic in the form:
Remember that we had the other root,