All categories

3 years ago

Write a polynomial function of the least degree that has roots of 3 and (4 + i).

Mathematics

1 answer:

polet [3.4K]3 years ago

4 0

Answer:

x³ - 11x² + 41x - 51

Step-by-step explanation:

The least number of degree is 3 and the third root should be (4 - i) to make polynomial rational.

The polynomial is:

(x - 3)(x - (4 + i))(x - (4 + i)) =
(x - 3)(x² -x(4 + i + 4 - i) + (4 + i)(4 - i)) =
(x - 3)(x² - 8x + 16 - (-1)) =
(x - 3)(x² - 8x + 17) =
x³ - 8x² + 17x - 3x² + 24x - 51 =
x³ - 11x² + 41x - 51

You might be interested in

Solve using the quadratic equation 3x^2 -7x -3=0

strojnjashka [21]

Answer: x=7/6+1/6^85 or x=7/6+−1/6^85

Step-by-step explanation: hope this help

3 0

3 years ago

The perimeter of a rectangle is 132 feet and its area is 1080 square feet. find the dimensions

FrozenT [24]

2x + 2y=132

xy=1080

Let x=1080/y

2160/y + 2y=132
2y^2 - 132y +2160=0
2(y^2-66y+1080)=0
2(y-30)(y-33)=0
y=30 or y=33
(36,30) or (30,36)

So... x=30,36 and y=36,30. Either way, the answer is 30 by 36 or 36 by 30.

5 0

3 years ago

Eliza started the week with $274 in her bank account. This week she babysat for 16 hours and made $144.25. Eliza then went to th

elixir [45]

Hi. I hope this helps!

I believe the answer is 330.26 left.

1. First you add 274 and 144.25

You get 388.25

2. The. You subtract the amount of the video game from 388.25

You get 330.26

I hope this helps! Have a great day!

4 0

4 years ago

Makers Corp. had additions to retained earnings for the year just ended of $205000. The firm paid out $185000 in cash divends, a

forsale [732]

Answer:

3.9

Step-by-step explanation:

The retained earnings for the year is $205,000

The firm paid out $185,000 in cash dividend

It has total equity of$4.90 million

100,000 common shares are outstanding

Therefore the earnings per share van be calculated as follows

= 205,000+185,000/100,000

= 390,000/100,000

= 3.9

Hence the earnings per share is $3.9

6 0

3 years ago

1. Find the slope of the line that goes through the points (2, 5) and (6, 7)

ella [17]

Answer:

$\displaystyle m = \frac{1}{2}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)
Slope Formula: $\displaystyle m = \frac{y_2-y_1}{x_2-x_1}$

Step-by-step explanation:

Step 1: Define

Identify

Point (2, 5)

Point (6, 7)

Step 2: Find slope m

Substitute in points [Slope Formula]: $\displaystyle m = \frac{7-5}{6-2}$
[Fraction] Subtract: $\displaystyle m = \frac{2}{4}$
[Fraction] Simplify: $\displaystyle m = \frac{1}{2}$

7 0

3 years ago