SOLUTION: Find a 4th degree polynomial fucntions f(x) with real coefficients that has 3,4, and i as zeros and such that f(1)=24

Question 531951: Find a 4th degree polynomial fucntions f(x) with real coefficients that has 3,4, and i as zeros and such that f(1)=24
Answer by la080360(1) (Show Source): You can put this solution on YOUR website!
f(x)= A(x+i)(x-i)(x-3)(x-4)
f(x)= A(x^2+i^2)(x^2-4x-3x+12)
f(x)= A(x^2+1)(x^2-7x+12)
_______________________________
f(1)=24
f(1)=A((1^2+1)(1^2-7(1)+12))
f(1)=A(1+1)(1-7+12)
f(1)=A(2)(6)
f(1)=A(12)=24
A(12)=24
divide both sides by 12 to get A by itself
A=2
________________________________
Plug A into the formula f(x)=A(x^2+1)(x^2-7x+12)
f(x)=2((x^2+1)(x^2-7x+12))
combine (x^2+1) with (x^2-7x+12) by using the FOIL method
f(x)=2(x^4-7x^3+12x^2+x^2-7x+12)
f(x)=2(x^4-7x^3+13x^2-7x+12)
distribute the value of A=2 to get your FINAL answer!
ANSWER: f(x)=2x^4-14x^3+26x^2-14x+24

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