Polynomial Graphs with Real and Complex Roots

• 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.

Imagine Mason is analyzing a polynomial function f(x) = x^4 - 12x + 1 as part of his mathematics project. Including all real and imaginary solutions, how many solutions exist for this function?

• 0

• 1

• 2

• 4

William is analyzing a quadratic polynomial in his math class. Which statement is true about the zeros of this polynomial?

• The polynomial can have a maximum of 2 real zeros.

• There must be at least one complex zero for every real zero.

• If -5 and 4 are zeros, then the conjugates of -5 and 4 must also be zeros.

• If the polynomial has 3 zeros, it must have imaginary coefficients.

How many complex or "imaginary" solutions?

• 1

• 2

• 4

• 10

• The function has 5 real roots
• The function has 4 complex roots
• The function has 3 complex roots
• The function has no complex roots

What are the roots of

the graph to the right?

• -3, 1, and 6

• -2, 1, and 6

• -2, 2, and 6

• 2, 1, and 6

How many real zeros does the function have?

• None

• 2

• 3

• 4

• 2
• 1
• 3
• None

What are the zeros of the function?

• 4,1

• 3,1,-2,-5

• -3, -1, 2, 5

• -2,4