Question
Find the polynomial function f with Real coefficients that has the given degree 3 zeros -2, 1-sqrt 2i, and solution point -42
Answers
oobleck
since complex roots come in conjugate pairs,
f(x) = a(x+2)(x-(1-i√2))(x-(1+i√2))
= a(x+2)((x-1)^2+2)
Not sure what a "solution point" is, since you have already given the roots.
But if f(0) = 42, then
a(2)(1+2) = 42
a = 7
and f(x) = 7(x+2)(x^2-2x+3)
f(x) = a(x+2)(x-(1-i√2))(x-(1+i√2))
= a(x+2)((x-1)^2+2)
Not sure what a "solution point" is, since you have already given the roots.
But if f(0) = 42, then
a(2)(1+2) = 42
a = 7
and f(x) = 7(x+2)(x^2-2x+3)