algebra 2 help - polynomials, roots?

1. By Rational Root Theorem, you have:

{±factors of last term/factors of first term}

{±1,2/1}

Apply synthetic division. Assume that one of the roots is 1.

1...-1...2...-2

......1...0....2

1....0...2....0

This gives:

x² + 2 = 0

Solving for x for x² + 2 gives imaginary roots. Therefore, the root is 1.

This is similar to last two problems.

2. x³ + 2x² - 8x - 16 = 0

{±1,2,4,8,16/1}

Assume that the root -2 works.

1...2...-8...-16

....-2....0....16

1...0...-8....0

This gives:

x² - 8 = 0

You can solve for x for x² - 8, which gives:

x = {±2√2}

The roots are ±2√2 and -2.

3. 2x^4 - 5x³ - 17x² + 41x - 21 = 0

{±1,3,7,21/1,2}

Assume that -3 works.

2...-5...-17...41...-21

.....-6....33..-48...21

2...-11..16..-7.....0

This gives:

2x³ - 11x² + 16x - 7 = 0

Apply Rational Root Theorem and synthetic division again!

{±1,7/1,2}

Assume that 1 works.

2...-11...16...-7

......2......-9....7

2....-9......7....0

This gives:

2x² - 9x + 7 = 0

Factor.

(2x - 7)(x - 1) = 0

Set each by zero.

2x - 7 = 0 and x - 1 = 0

This gives:

x = {7/2,1}

Overall, you have:

x = {1, -3, 7/2}

I hope this helps!

If youre attempting to make a function, and you have been given (2 + i), i = ?-a million And sq. roots constantly are available in valuable and detrimental pairs, so i (as a effect) = ±?-a million So foil (2+i)(2-i) and thats your answer.