Question

What information must you have to write a polynomial function having all real roots given its graph?

Answer 1

I'm not 100% sure I know what you're asking, but if you know all points in an interval (from the graph) then you can find all derivatives in that point and then determine the polynomial using a Taylor expansion.

Answer 2

Oh now I get it.

Answer 3

yea that is what im asking thanks

Answer 4

I have another answer. If you know all the roots by knowing the graph then you need to know the multiplicity of each root and a constant \(k\) by which you scale \((x-x_1)(x-x_2)...(x-x_n)\), where \(x_i\) is the \(i\)th root with repetition, to get the polynomial.

Answer 5

The degree is \(n\).