Writing Polynomial Functions from Complex Roots

Question 1

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 2

Which polynomial function could be represented by the graph below?

Revolt · Accepted Answer

f(x) = –2x3 – 2x2 + 12x

Question 3

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 4

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 5

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 6

Which polynomial function could be represented by the graph below?

Revolt · Accepted Answer

f(x) = 3x2 – 18x + 24

Question 7

If a polynomial function f(x) has roots –9 and 7 – i, what must be a factor of f(x)?

Revolt · Accepted Answer

(x – (7 + i))

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

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

Revolt · Accepted Answer

x + 6

Question 10

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

Writing Polynomial Functions from Complex Roots Answers