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If p(x) is a polynomial such that p(0)=5 ,p(1)=4 ,p(2)=9,p(3)=20 ,
the minimum degree it can have
the minimum degree it can have
jacks said:If p(x) is a polynomial such that p(0)=5 ,p(1)=4 ,p(2)=9,p(3)=20 ,
the minimum degree it can have
Plotting the four points, a parabola might pass through them.If p(x) is a polynomial such that: .p(0) = 5,\;p(1) = 4,\;p(2) = 9,\;p(3) = 20,
. . the minimum degree it can have is __.
Then polynomial, passing through four given points, will have degree at most three, not "at least". It is quite possible that the four points happen to lie on a parabola (which is apparently the case here) or even on a straight line.Prove It said:You have four points, so for them to fit the polynomial exactly, you need it to at least have degree three. Anything more you'll have an infinite number of possibilities that will have all data points fit, and anything less then chances are you'll only be able to get a least squares approximation.
HallsofIvy said:Then polynomial, passing through four given points, will have degree at most three, not "at least". It is quite possible that the four points happen to lie on a parabola (which is apparently the case here) or even on a straight line.
Prove It said:Really? I would have thought that there would be an infinite number of solutions to, say, four equations in five unknowns, which is what you would get if you substituted the four points into a general polynomial of degree 4...