All categories

2 years ago

Find a degree 3 polynomial having zeros -5, 1 and 5 and the coefficient of x^3 equal 1

Mathematics

1 answer:

mote1985 [20]2 years ago

7 0

Answer:

$x^3 -x^2 -25x +25$

Step-by-step explanation:

$\text{The roots are,}~ \alpha = -5,~ \beta = 1 ~ \text{and}~ \gamma = 5\\\\\text{The polynomial is,}\\\\~~~x^3 - (\alpha + \beta + \gamma)x^2+(\alpha \beta + \beta \gamma+ \gamma \alpha)x - \alpha\beta \gamma\\\\=x^3 - (-5+1+5)x^2 +(-5 \cdot 1 + 1 \cdot 5 + 5 \cdot -5)x - (-5)(1)(5)\\\\=x^3 -(0+1)x^2 + (-5+5-25)x +25\\\\=x^3 -x^2 -25x +25$

You might be interested in

Juan graphed a line with a slope of −23 .

Licemer1 [7]

Answer:

The answer is: From any point on the graph, he counts down 2 then right 3 to end up on the line again.

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Please help 25 points

algol13

Answer:

(-1,5)

(3, 1/125)

Step-by-step explanation:

g(x) = (1/5) ^x

Lets check the points

(1,0)

0 = (1/5) ^1

0 = 1/5 False this is not on the graph

(-1,5)

5 = (1/5) ^ -1

Remember negative exponents flip the fraction inside the parentheses

5 = 5/1 True this is on the graph

(3, 1/125)

1/125 = (1/5)^ 3

1/125 = 1^3/ 5^3

1/125 = 1/125 true this is on the graph

(-2,1/25)

1/25 = (1/5) ^-2

Remember negative exponents flip the fraction inside the parentheses

1/25 = 5^2/1^2

1/25 = 25 false this is not on the graph

4 0

3 years ago

A special discount was offered to the employees of Ryan's, a lead ing men's store. Employees were given their employee discount

Helen [10]

Answer: a) $2155, b) $1763.03.

Step-by-step explanation:

Since we have given that

Number of cable knit sweaters = 15

Cost per sweaters = $65.00

Number of pairs of khaki twill pants = 22

Cost of each pair = $50.00

Number of casual jackets = 18

Cost of each jackets = $62.00

total sale volume would be

$15\times 65+22\times 50+18\times 62\\\\=\$3191$

Employee discount = 35%

Additional discount = 15%

So, Total markdown dollars taken is given by

$3191\times \dfrac{100-35}{100}\times \dfrac{100-15}{100}\\\\=3191\times \dfrac{65}{100}\times \dfrac{85}{100}\\\\=3191\times 0.65\times 0.85\\\\=\$1763.0275$

Hence, a) $2155, b) $1763.03.

4 0

3 years ago

An agricultural company called Phatsima Pty. Ltd. owns an rectangular fuel tank that measures 75 cm by 65 cm by 30 cm.

GaryK [48]

I believe that A is the answer. We can solve this by multiplying 75cm, 65cm and 30cm together. This would give us 146,250.00ml. We can then divide 146,250.00 by 1000 to receive 146.25. We then divide 146.25 by 2 to calculate how many litres there are in half a tank. This would result in 73.125. After that, we multiple 73.125 by the cost of the fuel, which is R20.35. We then receive R 1,480.09375, which can be rounded to R 1,480.10

3 0

1 year ago

CONSTRUCTION Carlos is building a screen door. The height of the door is I foot more than twice its width. What is the width of

-BARSIC- [3]

Answer:

<h2>width = 3 feet</h2>

Step-by-step explanation:

Let h be the height of the door

and w be its width

The statement “The height of the door is I foot more than twice its width”

can be translated mathematically like this : h = 2w + 1

Let’s solve the equation for w:

h = 2w + 1

⇔ 2w = h - 1

$\Leftrightarrow w=\frac{h-1}{2}$

now , if the door is 7 feet high then it’s width is equal to :

$\Rightarrow \frac{7-1}{2} =\frac{6}{2} =3 \ ft$

6 0

1 year ago

Read 2 more answers