[True/False]The polynomial $x^4+7x^3−13x^2+11x$ has exactly one real root.
I want to solve it without drawing the graph. Here is my idea. Note that $f(1)=1+7-13+11=6>0$ and $f(-1)=1-7-13-11=-30<0$
So we have at least one real root. Now since degree is $4$ we have $4$ roots but rest three can not be complex as they occur in pairs, so we must have another real root.
So the statement is False
Am I right?
Thanks for reading and all the help.