Writing Polynomial Functions from Complex Roots

Question 1

Which polynomial function could be represented by the graph below?

Revolt · Accepted Answer

f(x) = 3x2 – 18x + 24

Question 2

What is the polynomial function of lowest degree with lead coefficient 1 and roots i, –2, and 2?

Revolt · Accepted Answer

f(x) = x4 – 3x2 – 4

Question 3

What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?

Revolt · Accepted Answer

x – 1

Question 4

What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?

Revolt · Accepted Answer

x + 6

Question 5

Which polynomial function has a leading coefficient of 1 and roots 2i and 3i with multiplicity 1?

Revolt · Accepted Answer

f(x) = (x + 2i)(x + 3i)(x – 2i)(x – 3i)

Question 6

Which second degree polynomial function has a leading coefficient of –1 and root 4 with multiplicity 2?

Revolt · Accepted Answer

f(x) = –x2 + 8x – 16

Question 7

Which polynomial function could be represented by the graph below?

Revolt · Accepted Answer

f(x) = –2x3 – 2x2 + 12x

Question 8

Which polynomial function has a leading coefficient of 1 and roots (7 + i) and (5 – i) with multiplicity 1?

Revolt · Accepted Answer

f(x) = (x – (7 – i))(x – (5 + i))(x – (7 + i))(x – (5 – i))

Question 9

Which polynomial function f(x) has a leading coefficient of 1, roots –4, 2, and 9 with multiplicity 1, and root –5 with multiplicity 3?

Revolt · Accepted Answer

f(x) = (x + 5)(x + 5)(x + 5)(x + 4)(x – 2)(x – 9)

Question 10

If a polynomial function f(x) has roots 4 – 13i and 5, what must be a factor of f(x)?

Revolt · Accepted Answer

(x – (4 + 13i))

Writing Polynomial Functions from Complex Roots Answers