SOLUTION: find an nth degree polynomial function with real coefficients satisfying the given conditions. n = 3; 3 and i are zeros; f(2) = 30

Question 193530This question is from textbook
: find an nth degree polynomial function with real coefficients satisfying the given conditions. n = 3; 3 and i are zeros; f(2) = 30 This question is from textbook

Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
zeros are 3,3,i
factors are (x-3)(x-3)(x^2+1)
distributing
(x^2+1) (x^2-6x+9)
distributing further
x^4-6x^3+9x^2 +x^2 -6x+9
simplify
x^4-6x^3+10X^2-6x+9
if Y(2)=30,,,lets see have how above calculates
Y(2)= (2)^4 -6(2)^3+10(2)^2-6(2)+9=5
therefore we need to multiply all terms by 6 (5*6=30)
y(x)= 6x^2 -36x^3+60x^2-36x+54,,,,ANSWER
calculating as above Y(2)=30
y(2)=6(2)^4-36(2)^3+60(2)^2-36(2)+54=30
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