Algebra I Roots Solutions

Can a 7th degree polynomial have 0 real roots?

• No, it must have at least 1 real root.

• Yes, but only if it has 7 non-real complex roots.

• No, the Fundamental Theorem of Algebra does not allow this.

• Yes, if all roots are complex.

What are the zeros of the function f(x) = x² + 64?

• -8 and 8

• -8i and 8i

• (-√8) i and (√8) i

• -√8  and √8

Which the following function is matching the give graph

Use the Fundamental Theorem of Algebra to determine the total number of solutions.

• A

• B

• C

• D

Find ALL zeros

• A

• B

• C

• D

How many roots or zeros does the equation
f(x) = 5x⁴-8x³+4x²-6x+3 have?

• 3

• 4

• 5

• 0

⅖(x + 3)² + 8 = -32

• x = 3 ± 10i

• x = ±13i

• x = -3 ± 10i

• x = ±i√10

What is the least degree of the following polynomial that has 4 real roots and 2 imaginary roots?

• 4

• 2

• 8

• 6

Write the polynomial in standard form given the following zeros. x = -2, 1, 4

• f(x) = (x+2)(x-1)(x-4)

• f(x) =x³ - 3x² - 6x + 8

• f(x) = x³ + 8

• f(x) = x³ - 3x² + 8

Can a 7th degree polynomial have 9 real roots?

• Yes, but only if some roots are complex.

• Yes, if all roots are distinct.

• No, it must have exactly 7 complex roots.

• No, it can have at most 7 real roots.