Writing Polynomial Functions from Complex Roots

Question 1

A polynomial function with a leading coefficient of 1 and multiplicity 1 for each factor has the following roots:x–2, x–(1+ StartRoot 5 EndRoot ), x+3iAnother factor of the polynomial is:

Revolt · Accepted Answer

x-(1-)

Question 2

The complex conjugates theorem states that another factor of the polynomial is 3ixx + 2x – 3i.

Revolt · Accepted Answer

– 3i

Question 3

What is the degree of the polynomial?

Revolt · Accepted Answer

5

Question 4

A polynomial function with a leading coefficient of 1 and multiplicity 1 for each factor has the following zeroes: How many total factors does the polynomial have?

Revolt · Accepted Answer

1

Question 5

Which is the polynomial function of lowest degree that has –5, –2, and 0 as roots?

Revolt · Accepted Answer

f(x) = x(x + 2)(x + 5)

Question 6

Which of the following could represent the function shown in the graph?

Revolt · Accepted Answer

f(x) = (x + 4)(x – 1)(x – 3)

Question 7

A polynomial has x-intercepts of 3, 0, and –1, and passes through the point (1, –8). Which of the following functions could represent this graph?

Revolt · Accepted Answer

2x3 – 4x2 – 6x

Question 8

Which is the polynomial equation of lowest degree that has –10, –1, 3, and 4 as roots?

Revolt · Accepted Answer

f(x) = (x + 10)(x + 1)(x – 3)(x – 4)

Question 9

What is the polynomial function?

Revolt · Accepted Answer

f(x) = x4 – 4x3 + 3x2 + 8x – 10

Question 10

The cubic function shown by the graph is

Revolt · Accepted Answer

x3 – 13x + 12

Writing Polynomial Functions from Complex Roots Answers

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