SOLUTION: 1. ​​Use what you have learned to find the solutions of the polynomial equation shown below. x4 + 5x3 ‒ x2 ‒ 50x ‒ 90 = 0 if x2 ‒ 10 is one

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: 1. ​​Use what you have learned to find the solutions of the polynomial equation shown below. x4 + 5x3 ‒ x2 ‒ 50x ‒ 90 = 0 if x2 ‒ 10 is one       Log On


   

Question 1032244: 1. ​​Use what you have learned to find the solutions of the polynomial equation shown below.
x4 + 5x3 ‒ x2 ‒ 50x ‒ 90 = 0 if x2 ‒ 10 is one of the factors.
Be sure to discuss real and complex solutions and how these solutions will affect the graph of the polynomial equation.

2. Use what you have learned in this lesson to determine all of the values for k that would give complex solutions to the equation shown below.
3x2 ‒ 8x + k = 0
Describe how you know your values for k give complex solutions to the equation.
Then, write a quadratic equation using a value of k that will have complex solutions and solve.

(Note: Please show your work so that I can understand your logic. Thank you.)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
1:

Use polynomial division (unless you know synthetic division for that kind of divisor). The quotient will be quadratic, and you can then either factor it or use general solution for quadratic formula to get the roots.


2:

3x%5E2-8x%2Bk=0
If you want complex solutions with imaginary parts, then use discriminant related to less than 0.
-
%28-8%29%5E2-4%2A3%2Ak%3C0
Solve this statement for k.
-12k%2B64%3C0
-12k%3C-64
k%3E64%2F12
k%3E32%2F6
highlight%28k%3E16%2F3%29