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miss Akunina [59]
3 years ago
11

Write a polynomial in standard form with zeros at -2 and 3 !!!!! PLZ HELP

Mathematics
2 answers:
just olya [345]3 years ago
5 0
The answer is X^2 - X - 6
lara31 [8.8K]3 years ago
3 0

If the zeros are -2 and 3, then the factored form would be

(x+2) and (x-3)  

-2+2 = 0 and 3-3 = 0

A polynomial is written as ax^2 + bx + c

Expand (x+2) (x-3) using FOIL: Multiply each tern in one set of parenthesis by each term in the other set and then simplify by combining like terms:

x*x + x*-3 + 2*x + 2*-3

x^2 -3x + 2x -6

Polynomial in standard form:

x^2 -x -6

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The width of a rectangle is 6 kilometers less than twice its length. if its area is 108 square​ kilometers, find the dimensions
Art [367]
Hi there!

Answer:
length = 9 kilometres
Width = 12 kilometres

Let's solve this problem step by step!
To find our answer we need to set up and solve an equation.

Let the length of the rectangle be represented by x.
The width of the rectangle can therefore be expressed by 2x - 6.

The area of a rectangle can be found by using the formula:
A = width × length

Plug in the data from the formula
A = x (2x - 6).

Simplify using rainbow technique.
x(2x - 6) = 2 {x}^{2} - 6x

Now we've found the simplified expression that expresses the area of the rectangle. Therefore, we can now set up and start solve the equation.

2 {x}^{2} - 6x = 108
Subtract 108

2 {x}^{2} - 6x - 108 = 0
Divide by 2.

{x}^{2} - 3x - 54
(x - 9)(x + 6) = 0
Rule AB = 0, gives A is 0 or B is 0.

x - 9 = 0 \\ x = 9 \\ \\ x + 6 = 0 \\ x = - 6

The length of the rectangle, which was represented by x, must be 9 (since it cannot be a negative number).

Length
x = 9
Width
2x - 6 = 2 \times 9- 6 = 18 - 6 = 12

Answer:
length = 9 kilometres
Width = 12 kilometres

~ Hope this helps you!
6 0
3 years ago
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