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 ->  Sequences-and-series -> 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 1033715: 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.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
1:
Use polynomial division and the other quadratic factor will be the quotient of this division. Factorize this if possible either simple trial combinations or using general solution for quadratic formula. Note that if discriminant is negative, then its solutions are complex with imaginary parts.

2:
If you want non-real, complex solutions, then the discriminant must be negative, or %28-8%29%5E2-4%2A3%2Ak%3C0 and you can solve for k. Pick any acceptable value for k to write a more specific quadratic equation.