Finding Real and Complex Roots of Polynomials

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

• A
• B
• C
• D

Tags

CCSS.HSN.CN.C.9

Find the zeros of the polynomial.
f(x) = (x-5)(2x+3)(7x-4)(x+6)

• x = 5, (2/3), 6, (7/4)
• x= -5, (3/2), (-4/7), 6
• x= 5, (-3/2), (4/7), -6
• x= 6, 5, -2/3, -4/7

Tags

CCSS.HSF-IF.C.7C

Given one complex zero use the conjugate root theorem to find another.  Zero is 7-5i

• -7+5i
• 7-5i
• -7-5i
• 7+5i

Tags

CCSS.HSN.CN.A.3

What are the zeros of the function?

• 4,1
• 3,1,-2,-5
• -3, -1, 2, 5
• -2,4

Find a polynomial function of degree 3 that has zeroes at
x=1, 2, and 3

• x³ - 6x² + 11x - 6
• x³ - 11x² - 6x - 6
• x³ - 6x² - 6x - 6
• x³ - 11x² - 11x - 11

Tags

CCSS.HSA.APR.B.3

Find a polynomial function that has zeroes at
x=1+√2, 1-√2, and 1

• x³ - 3x² + x +1
• x³ - 3x² + 3x +1
• x³ - x² + x +3
• x³ - 3x² + 3x +3

Tags

CCSS.HSA.APR.B.3

The degree of the polynomial determines the number of roots.

• True
• False

All imaginary roots comes in pairs.

• True
• False

Tags

CCSS.HSN.CN.C.9

Which of the following would be the correct factored form with roots 2, 5i, and 6?

• (x-6)(x-2)(x+5i)(x-5i)

• (x+6)(x+2)(x+5i)

• (x-6)(x-2)(x-5i)

• (x+6)(x+2)(x-5i)

Tags

CCSS.HSA.APR.B.3

Find a polynomial function of degree 3 with zeros 3i and -2.

• P(x) = x³+2x²+9x+11
• P(x) = x³-2x²+9x+18
• P(x) = x³+2x²+9x+18
• P(x) = x²-3ix+2x-6i

Tags

CCSS.HSA.APR.B.3