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BaLLatris [955]
3 years ago
7

Identify all the real roots of 4x^4+31x^3-4x^2-89x+22=0

Mathematics
1 answer:
Vitek1552 [10]3 years ago
4 0
Solve for x over the real numbers:
4 x^4 + 31 x^3 - 4 x^2 - 89 x + 22 = 0

The left hand side factors into a product with three terms:
(x + 2) (4 x - 1) (x^2 + 6 x - 11) = 0

Split into three equations:
x + 2 = 0 or 4 x - 1 = 0 or x^2 + 6 x - 11 = 0

Subtract 2 from both sides:
x = -2 or 4 x - 1 = 0 or x^2 + 6 x - 11 = 0

Add 1 to both sides:
x = -2 or 4 x = 1 or x^2 + 6 x - 11 = 0

Divide both sides by 4:
x = -2 or x = 1/4 or x^2 + 6 x - 11 = 0

Add 11 to both sides:
x = -2 or x = 1/4 or x^2 + 6 x = 11

Add 9 to both sides:
x = -2 or x = 1/4 or x^2 + 6 x + 9 = 20

Write the left hand side as a square:
x = -2 or x = 1/4 or (x + 3)^2 = 20

Take the square root of both sides:
x = -2 or x = 1/4 or x + 3 = 2 sqrt(5) or x + 3 = -2 sqrt(5)

Subtract 3 from both sides:
x = -2 or x = 1/4 or x = 2 sqrt(5) - 3 or x + 3 = -2 sqrt(5)

Subtract 3 from both sides:
Answer:  x = -2 or x = 1/4 or x = 2 sqrt(5) - 3 or x = -3 - 2 sqrt(5)
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27

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Ms. Lynch has 21 coins in nickels and dimes. Their total value is $1. 65. How many of each coin does she have? Please answer!!
timama [110]

Hi, there

<u>Question:Ms. Lynch has 21 coins in nickels and dimes. Their total value is $1. 65. How many of each coin does she have?</u>

Explanation:

1.65 x 21

Answer 34.65

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Find the area of this figure. Please show work if you can!
Yuri [45]
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8 0
3 years ago
The perimeter of a rectangle is 34 units. Its width is 6.5 point, 5 units.
12345 [234]
<h3><u>Question:</u></h3>

The perimeter of a rectangle is 34 units. Its width W is 6.5 units.

Write an equation to represent the perimeter in terms of the length L, and find the value of L

<h3><u>Answer:</u></h3>

The length of rectangle is 10.5 units

<h3><u>Solution:</u></h3>

Given that,

Perimeter of rectangle = 34 units

Width of rectangle = 6.5 units

Let "L" be the length of rectangle

<em><u>The perimeter of rectangle is given by formula:</u></em>

Perimeter = 2(length + width)

<em><u>Substituting the values we get,</u></em>

34 = 2(L + 6.5)

Thus the equation is found

<em><u>Solve for "L"</u></em>

L + 6.5 = \frac{34}{2}\\\\L + 6.5 = 17\\\\L = 17 - 6.5\\\\L =10.5

Thus length of rectangle is 10.5 units

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3 years ago
T 11 is 12% of what number?
zmey [24]

Answer:

88

Step-by-step explanation:

12.5% is the same as 1/8 of something

11*8=88

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2 years ago
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