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

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) (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 and you can solve for k. Pick any acceptable value for k to write a more specific quadratic equation.
RELATED QUESTIONS
1. Use what you have learned to find the solutions of the polynomial... (answered by josgarithmetic)

1. Sketch the graph of the polynomial function f(x) = ‒x4 + 5x3 + 9x2 ‒ 45x... (answered by KMST)

Evaluate the discriminant for the following... (answered by josgarithmetic)

Find an equation of the line passing through the given points. Use function notation to... (answered by Alan3354)

The graph of the function h(x) is shown. Find the function values... (answered by josgarithmetic)

The average, or mean, D, of three exam grades, w,... (answered by Boreal)

Question Help Think About the Process A jar contains only... (answered by stanbon)

In a round-robin chess tournament, each player is paired with every other... (answered by ikleyn)

In a community garden (shown to the right) you want to plant and fence in a (answered by Fombitz)

SOLUTION: 1. &#8203;&#8203;Use what you have learned to find the solutions of the polynomial equation shown below. x4 + 5x3 &#8210; x2 &#8210; 50x &#8210; 90 = 0 if x2 &#8210; 10 is one

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