This is for review for my final exam. I would like to learn how to grasp the concept and answer the problem correctly, so please explain each step.
Find a 3rd degree polynomial function with real coefficients satisfying the given conditions.
-4 and i are zeros; f(2) = 90
thank you in advance & will choose best answer!
Find a 3rd degree polynomial function with real coefficients satisfying the given conditions.
-4 and i are zeros; f(2) = 90
thank you in advance & will choose best answer!
-
complex/imaginary solutions come in conjugate pairs...if " i " is a zero, then " - i " is too !
f(x) = a(x + 4)(x + i_)(x - i) = a(x + 4)(x^2 + 1) = a(x^3 + 4x^2 + x + 4)
now, solve for a: you know that f(2) = 90
so,
f(2) = 90 = a(x^3 + 4x^2 + x + 4) = a(8 + 16 + 2 + 4) = a(30)
a = 3
the funciton is: f(x) = 3x^3 + 12x^2 + 3x + 4
check
qed
f(x) = a(x + 4)(x + i_)(x - i) = a(x + 4)(x^2 + 1) = a(x^3 + 4x^2 + x + 4)
now, solve for a: you know that f(2) = 90
so,
f(2) = 90 = a(x^3 + 4x^2 + x + 4) = a(8 + 16 + 2 + 4) = a(30)
a = 3
the funciton is: f(x) = 3x^3 + 12x^2 + 3x + 4
check
qed