Writing Polynomial Functions from Complex Roots

Question 1

If a polynomial function, f(x), with rational coefficients has roots 3 and , what must also be a root of f(x)?

Revolt · Accepted Answer

Negative StartRoot 7 EndRoot

Question 2

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 3

If a polynomial function, f(x), with rational coefficients has roots 0, 4, and , what must also be a root of f(x)?

Revolt · Accepted Answer

3 minus StartRoot 11 EndRoot

Question 4

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 5

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 6

Which polynomial function has a leading coefficient of 3 and roots –4, i, and 2, all with multiplicity 1?

Revolt · Accepted Answer

f(x) = 3(x + 4)(x – i)(x + i)(x – 2)

Question 7

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))

Question 8

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

Revolt · Accepted Answer

x + 6

Question 9

If a polynomial function f(x) has roots –8, 1, and 6i, what must also be a root of f(x)?

Revolt · Accepted Answer

–6i

Question 10

Which polynomial function could be represented by the graph below?

Revolt · Accepted Answer

f(x) = 3x2 – 18x + 24

Writing Polynomial Functions from Complex Roots Answers