Suppose I have a equation of a degree of 4 and I don't know a proper method of solving this type of equation (like completing the square is a proper method to solve the quadratic equation) so how or what necessary steps should I follow so that I could guess more precisely the roots of such equation.
I asked this question because I encountered a problem in a competitive exam which asked to tell the number of distinct real roots of a equation of degree 4.
the question being:
the number of distinct real roots of $x^4-4x^3+12x^2+x-1=0 $ is $\_\_\_\_\_$
We all know that a polynomial of degree n can have maximum n roots. So the above equation can have maximum 4 roots. So I wrote 4 as the answer since there was no negative marking but I checked out by making the graph of this equation in a graph calculator which showed that this equation has 2 roots. So if would know how to find out the roots then it could reward me more marks.
So what should be done?