Good day all,
I have an example in my book that ask:
For which values of k, if any, does $x^3−3x^2+6x+k=0$ have 3 real roots?
I know that this is a quadratic equation and that normally I would need to take the derivative of this equation and set it equal to zero and use the quadratic formula to find the x values.
However the books states that because $6^2$ < 4 x 3 x 6, it can have no real roots. I am for some reason not able to grasps the explanation given here. If someone could point me in the right direction or explain where they are getting $6^2$ < 4 x 3 x 6, it would greatly be appreciated.
I am using the book "Mathematical Methods for Physics and Engineering" by Riley, Hobson and Bence.
Thank you in advance.