Hi, I need help please it's due today, but I don't get it

Question

Given the zeros in each problem, use factors to find the original polynomial

1. -1, 1+3i
2. -1/4, 1+√6
3. 1+√3, -3+√5

THEY ARE WRITTEN CORRECTLY. PLEASE HELP ME WITH ALL THE PROBLEMS THANK YOU :)

Answer 1

Hi, I need help please it's due today, but I don't get it

Given the zeros in each problem, use factors to find the original polynomial

-1, 1+3i

-1/4, 1+√6

1+√3, -3+√5

THEY ARE WRITTEN CORRECTLY. PLEASE HELP ME WITH ALL THE PROBLEMS THANK YOU :)

Hello Kim,

Here you go...

-1, 1+3i

Remember that conjugates always come in pairs.

So, 1 + 3i comes with 1 - 3i

Now multiply them all together:

(x + 1)(x - (1 - 3i))(x - (1 + 3i))

foil these terms:

(x - (1 - 3i))*(x - (1 + 3i))

(x² - x(1 - 3i) - x(1 + 3i) + (1 - 3i)(1 + 3i))

Distribute x in the 2 middle terms, and foil the last two binomials:

(x² - x + 3xi - x - 3xi + (1² - 3i + 3i - 9i²)) ... * Recall that i² = -1

(x² - 2x + (1 - 9(-1)))

(x² - 2x + (1 + 9))

(x² - 2x + 10)

Now... Multiply (x² - 2x + 10) by the (x + 1) term:

........ x² - 2x + 10

................. x + 1

————————

......... x² - 2x + 10

+ x³ - 2x² + 4x

————————

x³ - x² + 2x + 10

For:

-1/4, 1+√6

Do the same process, since raidical always come in conjugate pairs too:

(x + 1/4)(x - (1+√6))( x - (1 - √6))

(x - (1+ √6)) (x - (1 - √6)) .....*Foil

x² - x(1 + √6) - x(1 - √6)) + (1 + √6)(1 - √6)

x² - x - x√6 - x + x√6 + (1² + √6 - √6 - 6)

x² - 2x + (1 - 6)

x² - 2x - 5

Now multiply by the (x + 1/4) term:

........ x² - 2x - 5

................. x + 1/4

—————————

...... 1/4x² - 1/2x - 5/4

+ x³ - 2x² - 5x

————————

x³ - 9/4x² -11/2x - 5/4

For 1+√3, -3+√5:

(x - (1+ √3))( x - (1 - √3))*(x - (-3+ √5))( x - (-3 - √5)) ..*FOIL both pairs:

1st Pair:

x² - x(1 + √3) - x(1 - √3)) + (1 + √3)(1 - √3)

x² - x - x√3 - x + x√3 + (1² + √3 - √3 - 3)

x² - 2x - 2

2nd Pair:

(x - (-3+ √5)) (x - (-3 - √5))

x² - x(-3 + √5) - x(-3 - √5)) + (-3 + √5)(-3 - √5)

x² + 3x - x√5 + 3x + x√5 + (3² - 3√5 + 3√5 - 5)

x² + 6x + 4

NOw multiply the two terms:

............ x² - 2x - 2

........... x² + 6x + 4

——————————

................. 4x² - 8x - 8

...... 6x³ - 12x² - 12x

x⁴ - 2x³ - 2x²

——————————

x⁴ + 4x³ - 10x² - 20x - 8

Any Question???

Answer 2

No, I will NOT do all of them.

If you cannot do any of them even with the help I am about to give, you should schedule a tutoring session.

For the first problem, the equation is

(x+1)(x-1+3i)(x-1-3i)=0