Question

Find a polynomial function with the given zeros, 0,0,0,sqrt6, -sqrt6

Answer 1

\[(x-0)(x-0)(x-0)(x-\sqrt{6})(x+\sqrt6)\]

Answer 2

Of course, \((x-0)(x-0)(x-0)=x^3\)

Answer 3

So would the answer be x^5-6x^3?

Answer 4

Yes, that is correct.

Answer 5

Yeah,,, thanks

Answer 6

Here's a plot showing the axis crossings at the roots of odd multiplicity

Answer 7

even multiplicity gets you a touching of the axis, but not a crossing

Answer 8

vertical lines indicate \(x=\pm\sqrt{6}\)