write a polynomial function of least degree with integral coefficients that has the given zeros.
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Answer:
x^3 -2x^2 -3x+6
Step-by-step explanation:
We have three roots
Using the root theorem
(x-sqrt(3)) (x- -sqrt(3)) (x-2)
(x-sqrt(3)) (x+sqrt(3)) (x-2)
We know that (x-a) (x+a) = x^2 -a^2
(x^2 -3)(x-2)
FOIL
first x^3
outer -2x^2
inner -3x
last 6
Add these together
x^3 -2x^2 -3x+6