Question
Find a polynomial with integer coefficients that satisfies the given conditions.
P has degree 2 and zeros
2 + i and 2 − i.
P has degree 2 and zeros
2 + i and 2 − i.
Answers
clearly, one such
P(x) = (x-(2+i))(x-(2-i))
= ((x-2)-i)((x-2)+i)
= (x-2)^2 - i^2
= x^2-4x+4 + 1
= x^2-4x+5
extra credit: why does the question imply that there is more than one such P(x)?
P(x) = (x-(2+i))(x-(2-i))
= ((x-2)-i)((x-2)+i)
= (x-2)^2 - i^2
= x^2-4x+4 + 1
= x^2-4x+5
extra credit: why does the question imply that there is more than one such P(x)?
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