Find all roots (x^4)-(3x^2)+4=0 Explain?

Question

Find all roots (x^4)-(3x^2)+4=0 Explain?

Answer 1

Notice that this is quadratic in x^2.  By that I mean that you could make a substitution to make it obviously quadratic.  Try y = x^2.  Then you have

y^2 - 3y + 4 = 0

This can be solved quite easily, either by factoring or using the Quadratic Formula.  Once you have the solutions to that one, resubstitute to get x.  For instance, if one of the solutions to the equation above is y = 9, then you know x^2 = 9 so x = +/- 3.