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inessss [21]
2 years ago
12

One of the five quadratics below has a repeated root. (The other four have distinct roots.) What is the repeated root?

Mathematics
1 answer:
pychu [463]2 years ago
6 0

Answer:

  (c)  8x^2 -32x +32, repeated root is x=2.

Step-by-step explanation:

A quadratic with repeated roots will be a multiple of a perfect square trinomial. The form of it will be ...

  a(x -b)² = ax² -2abx +ab² = a(x² -2bx +b²)

Dividing by the leading coefficient will leave a monic quadratic whose constant is a (positive) perfect square, and whose linear term has a coefficient that is double the root of the constant.

__

<h3>-x^2 + 18x + 81</h3>

Dividing by the leading coefficient gives ...

  x^2 -18x -81 . . . . . a negative constant

__

<h3>3x^2 - 6x + 9</h3>

Dividing by the leading coefficient gives ...

  x^2 -2x +3 . . . . . . constant is not a perfect square

__

<h3>8x^2 - 32x + 32</h3>

Dividing by the leading coefficient gives ...

  x^2 -4x +4 = (x -2)^2 . . . . . has a repeated root of x=2

__

<h3>25x^2 - 30x - 9</h3>

Dividing by the leading coefficient gives ...

  x^2 -1.2x -0.36 . . . . . . a negative constant

__

<h3>x^2 - 14x + 196</h3>

The x-coefficient is not 2 times the root of the constant.

  14 = √196 ≠ 2√196

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Jim wants to build a rectangular parking lot along a busy street but only has 2400 feet of fencing available. if no fencing is r
PSYCHO15rus [73]
<span>Length = 1200, width = 600
   First, let's create an equation for the area based upon the length. Since we have a total of 2400 feet of fence and only need to fence three sides of the region, we can define the width based upon the length as: W = (2400 - L)/2
   And area is: A = LW
    Substitute the equation for width, giving: A = LW A = L(2400 - L)/2
    And expand: A = (2400L - L^2)/2 A = 1200L - (1/2)L^2
    Now the easiest way of solving for the maximum area is to calculate the first derivative of the expression above, and solve for where it's value is 0. But since this is supposedly a high school problem, and the expression we have is a simple quadratic equation, we can solve it without using any calculus. Let's first use the quadratic formula with A=-1/2, B=1200, and C=0 and get the 2 roots which are 0 and 2400. Then we'll pick a point midway between those two which is (0 + 2400)/2 = 1200. And that should be your answer. But let's verify that by using the value (1200+e) and expand the equation to see what happens:
   A = 1200L - (1/2)L^2
 A = 1200(1200+e) - (1/2)(1200+e)^2
 A = 1440000+1200e - (1/2)(1440000 + 2400e + e^2)
 A = 1440000+1200e - (720000 + 1200e + (1/2)e^2)
 A = 1440000+1200e - 720000 - 1200e - (1/2)e^2
 A = 720000 - (1/2)e^2
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7 0
3 years ago
10) Show that in a group of 10 people (where any two people are either friends or enemies), there are either three mutual friend
ddd [48]

Answer with explanation:

Number of People in the group =10 People

The combination between two people is that, they can be either friends or enemies.

Total number of Possible Relation

                            =18 +16+14+12+10+8+6+4+2

                            = 90 Relations in all.

Out of 90 relations , 45 will be friends and 45 will be enemies.

⇒Now, we have to prove that, between 10 people, there are either three mutual friends or four mutual enemies, and there are either three mutual enemies or four mutual friends.

→→If there are three mutual friends, total number of people in the group =3 ×2=6 people in the group

And, four mutual enemies in a group means there are 2 people in each group.

So, total number of people if we combine the two groups in which there are either three mutual friends or four mutual enemies

   =6 +4

   =10

Hence proved.

→→→→Second part is ,in this group there can be either three mutual enemies or four mutual friends.

⇒If there are three mutual enemies, total number of people in the group =3 ×2=6 people in the group

And, four mutual friends in a group means there are 2 people in each group.

So, total number of people if we combine the two groups in which there are either three mutual enemies or four mutual enemies

   =6 +4

   =10

Hence proved.

3 0
3 years ago
I need help please help me
IrinaVladis [17]

Answer:

the first one

Step-by-step explanation:

To solve this problem you use the Triangle Angle Sum Theorem concept. Which means all 3 angles of a triangle add up to 180° degrees.

The formula for this concept is:

a+b+c=180°


5 0
3 years ago
Pleaseeee I need helppppp
77julia77 [94]

Answer:

v^32

Step-by-step explanation:

-4x-8=32

since it is a negative times a negative it becomes a positive

4 0
2 years ago
Read 2 more answers
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