Solving Polynomial Equations with Complex Solutions

Imagine Luna is working on a complex project involving polynomial equations. She encounters the equation 7x^4 - 5x^3 + 9x^8 + 10x - 6 = 0. How many solutions, including all real and imaginary solutions, does this equation have?

• 6

• 7

• 8

• 9

Scarlett is analyzing the function x^3 + 5x^2 + 21x - 16 in her mathematics project. She needs to determine the number and type of zeros for this function. How many and what type of zeros does the function have?

• 1 imaginary and 2 real solutions

• 2 imaginary and 1 real solutions

• 0 imaginary and 3 real solutions

• 3 imaginary and 0 real solutions

Oliver is studying polynomial functions in his mathematics class. He needs to determine which of the following polynomial functions have exactly 5 roots, including all real and imaginary roots. Can you help him?

• f(x) = 5x^4 + x^3 - x^2 + x - 5

• f(x) = 4x^5 + 3x^4 + 2x^3 + x^2 + x

• f(x) = 5x^6 - 5x^4 + 5x^2 - 5

• f(x) = 4x^4 - 3x^3 + 2x^2 - 1

• P has exactly two distinct real zeros and no non-real zeros.

• P has exactly three distinct real zeros.

• P has exactly four distinct real zeros.

• P has exactly two distinct real zeros and two non-real zeros.

Olivia is solving the equation x^2 - 4x = -8 in her math class. Which statement gives the number and type of solutions for this equation?

• The equation has one real solution.

• The solutions can only be determined by graphing.

• The equation has two real solutions.

• The equation has two nonreal complex solutions.

If b²-4ac is negative, the quadratic equation has:

• Two real solutions that are different

• Two imaginary solutions that are different

• A real double solution

• An imaginary double solution

What are the zeros of the function f(x) = x² + 64?

• -8 and 8

• -8i and 8i

• (-√8) i and (√8) i

• -√8  and √8

How does the quadratic equation show that there should be two complex solutions?

• b²

• ±

• b² - 4ac

• 2a

Find all the zeros, given that f(-3) = 0
f(x) = 2x³+5x²-6x-9

• -1,-3,-3

• -1,-3,3/2

• 3,3,3

• -3,2/3,-1