How do you find a polynomial of degree 3 that has zeros of -3, 0, 1?

1 Answer
sente
Nov 15, 2016

#P(x)=x^3+2x^2-3x#

Explanation:

A polynomial has #alpha# as a zero if and only if #(x-alpha)# is a factor of the polynomial. Working backwards, then, we can generate a polynomial with any zeros we desire by multiplying such factors.

We want a polynomial #P(x)# with zeros #-3, 0, 1#, so:

#P(x) = (x-(-3))(x-0)(x-1)#

#=(x+3)x(x-1)#

#=x(x+3)(x-1)#

#=x(x^2+2x-3)#

#=x^3+2x^2-3x#

Note that we could also multiply by any nonzero constant without changing the zeros, if a different polynomial is desired.

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