Gracelux
Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Find all zeros (real and complex) for the function f(x)=x^3-5x^2+9x-5

Sagot :

konrad509
[tex]f(x)=x^3-5x^2+9x-5\\ f(x)=x^3-x^2-4x^2+4x+5x-5\\ f(x)=x^2(x-1)-4x(x-1)+5(x-1)\\ f(x)=(x-1)(x^2-4x+5)\\\\ (x-1)(x^2-4x+5)=0\\\\ x-1=0\\ x=1\\\\ x^2-4x+5=0\\ x^2-4x+4+1=0\\ (x-2)^2=-1\\ x-2=i \vee x-2=-i\\ x=2+i \vee x=2-i\\\\ x=\{1,2-i,2+i\} [/tex]
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.