SOLUTION: given that 1+3i is a zero of f(x)= x^4-2x^3+5x^2+10x-50 find all zeros and write a linear factorization

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: given that 1+3i is a zero of f(x)= x^4-2x^3+5x^2+10x-50 find all zeros and write a linear factorization      Log On


   

Question 112257This question is from textbook Precalculus Graphical Numerical Algebraic
: given that 1+3i is a zero of f(x)= x^4-2x^3+5x^2+10x-50 find all zeros and write a linear factorization This question is from textbook Precalculus Graphical Numerical Algebraic

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
if 1+3i is a zero (root) then (x-1-3i) is a factor

since complex roots occur in conjugate pairs, (x-1+3i) is also a factor

so (x-1-3i)(x-1+3i) or x^2-2x+10 is a factor

(x^4-2x^3+5x^2+10x-50)/(x^2-2x+10)=x^2-5

this gives (x+sqrt(5)) and (x-sqrt(5)) as the two other factors