Precalc
posted by kelly .
find a possible polynomial equation of degree 4 if the zeroes are 1,2, and 5, the graph touches the xaxis at 1 but does not cross through, and the y intercept is 5

Precalc 
Reiny
there must be double root at x = 1
so it must be
y = a(x2)(x5)(x+1)^2
also we know (0,5) lies on it, so
5 = (2)(5)(1)
5 = 10a
a = 1/2
with your information there is a unique polynomial of
y = (1/2)(x2)(x5)(x+1)^2
expand if need be.
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