# How can I predict the value of the coefficients?

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Atony Garcia on 26 Jun 2020
Edited: Image Analyst on 28 Jun 2020
So I have this polynomial equation 𝑝(𝑥) = 𝑎 + 𝑎1𝑥 + 𝑎2𝑥^2 + 𝑎3𝑥^3 and it is cero when x = -2,1,3,4 and I need to answer with the values of the coefficients and proving that the answer is correct
I have tried this code but I am not sure if it is the right one:
p= [a a a a]
h =polyval([4 3 1 -2],0)
Thank you

Walter Roberson on 26 Jun 2020
Use polyfit() to compute p; the corresponding y would be 0.
You will probably think that the answer you get back from polyfit is incorrect, but it is correct under the condition that your cubic polynomial is zero at all four points x = -2,1,3,4
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Walter Roberson on 28 Jun 2020
what is your code and what is the error?. your x is [-2,1,3,4] and your y is all zeros.
Atony Garcia on 28 Jun 2020
Its the code I posted above in the first question

Image Analyst on 28 Jun 2020
Edited: Image Analyst on 28 Jun 2020
If you already know A, try roots with your given a vector.
x = roots([a(4), a(3), a(2), a(1)])
You should find x is [-2,1,3,4] if what it said was true.
You could also compute a Lagrange interpolating polynomial
y = (x- -2)*(x-1)*(x-3)*(x-4)
then multiply that out to find out the coefficients. Note that if you have x=0 at 4 locations, you can't do that with a cubic - you need a 4th order equation.