Polynomial problem

[thepilot]

A polynomial p(x) satisfies p(5-x) = p(5+x) for all real x. Suppose p(x) = 0 has four distinct real roots. Find the sum of these roots.

I am pretty good with polynomials, but I am confused about this one. I just don't understand how to go about it.

Any help is appreciated,
~tim

 

[Freeman]

P(x) is symmetric about x=5 and is of degree 4.
P(x)=a(x-5)⁴+b(x-5)²+c for some constants a,b,c.
Sum of roots = -coeff of x³/coeff of x⁴ =20.