Find the zeros for the given polynomial functions and give the multiplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero

f(x)=x^3-14x^2+14x

Question

Find the zeros for the given polynomial functions and give the multiplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero 

f(x)=x^3-14x^2+14x

anonymous · Answer

http://www.wolframalpha.com/input/?i=y+%3D+x%5E3-14x%5E2%2B14x+roots Clearly, x = 0 is a root, right? So we can factor out x from there to give: f(x) x(x^2 - 14x + 14). Solve the quadratic to get the other roots. The graph shows if they touch or turns around. :-)

anonymous · Answer

All roots have multiplicity 1, one of them is 0, the other two are 7 plus or minus sqrt(35) if my calculations are correct.