Polynomial Functions and Complex Zeros

Which statement gives the number and type of solutions for the 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 non-real complex solutions.

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NC.M3.N-CN.9

Including all real and imaginary solutions, how many solutions exist for thefunction

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NC.M3.N-CN.9

Which statement is true about the zeros of a quadratic 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.

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NC.M3.N-CN.9

The graph represents a polynomial function. What is the lowest possible degree of the polynomial?

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NC.M3.N-CN.9

Which statement is true about the polynomial?

• It has exactly 4 roots, including any repeated roots, that must be real numbers.

• It has exactly 8 roots, including any repeated roots, that must be real numbers.

• It has exactly 4 roots, including any repeated roots, that may be either real or complex numbers.

• It has exactly 8 roots, including any repeated roots, that may be either real or complex numbers.

Tags

NC.M3.N-CN.9

Tags

NC.M3.N-CN.9

Which of the following polynomial functions have exactly 5 roots, including all real and imaginary roots?

Tags

NC.M3.N-CN.9

Write a polynomial function of least degree with integral coefficients that has the given zeros.

• x³-5x²+4x-20

• x³-5x²+4x-23

• x³-5x²+4x-19

• x³-10x²+4x-20

Use the Complex Conjugate Root Theorem to state another complex solution. Given that 3+5i is a root. 

• -3+5i

• -3-5i

• -5i

• 3-5i

Use the Complex Conjugate Root Theorem to state another complex solution. Given that -7i is a root. 

• 7i

• -7i+1

• 1-7i

• 1+7i