How can I predict the value of the coefficients?

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

Answer 1

[Walter Roberson]

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

[Atony Garcia]

Thanks!

I have been trying to write it but its giving some errors, what is the correct way to do it?

[Walter Roberson]

what is your code and what is the error?. your x is [-2,1,3,4] and your y is all zeros.

[Atony Garcia]

Its the code I posted above in the first question

Answer 2

[Image Analyst]

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.