# Solve 2 4x  #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

##### Hello Guest!

It appears that you are browsing the GMAT Club forum unregistered!

• ### Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan Prep. All are free for GMAT Club members.

• ### Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application status, and more

Download thousands of study notes, question collections, GMAT Club’s Grammar and Math books. All are free!

### Hi GMATClubber!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

• We’ll give you
an estimate of

• We’ll provide
personalized question
recommendations

will be more realistic

### My Notes

#### Max: 2000 Characters x^2-4x<0 Inequalities [#permalink] May 29, 2020 9:58 am
What is the range for the inequality x^2 - 4x <0?

The solution is 0<x<4.

But I think the solution should be x<0 x>4.

Re: x^2-4x<0 Inequalities [#permalink] May 29, 2020 10:28 am
What is the range for the inequality x^2 - 4x <0?

The solution is 0<x<4.

But I think the solution should be x<0 x>4.

Hi happyapple123,

\(x^2 - 4x <0 => x (x - 4) < 0\)

This means either \(x < 0\) or \((x - 4) < 0\) but not both, because if both are negative then multiplication of two negative numbers is positive so the equation will not be true.

Now, if
\(x < 0\) then \((x - 4)\) is also less than 0, which makes both negative, so this cannot be true.

for example,

if \(x = -1\), then \((x - 4) => (-1 - 4) = -5 < 0\)
=> so, \((-1) * (-5) = 5 > 0\), so equation doesn't agree.

Hence, only \((x - 4) < 0\) but \(x > 0\) which means

\(0 < x < 4\) Re: x^2-4x<0 Inequalities [#permalink] May 29, 2020 11:44 am

##### GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.
###### © DeeP 2019 Web Design & Development Sours: https://gmatclub.com/forum/x-2-4x-0-inequalities-325450.html Basal Area: Definition & Formula

There are different ways to describe a stand of trees, one of which is basal area. In this lesson you'll learn about basal area, how to calculate it for a given tree, and why it's an important forestry assessment tool. Using Quadratic Formulas in Real Life Situations

This lesson will show us how to use the quadratic formula in real-life situations. We'll look at a couple of different real-world examples of when this formula can be used to solve problems that can be modeled using quadratic equations. SOHCAHTOA Examples Formula Rules

What is SohCahToa? Discover what SohCahToa stands for, learn SohCahToa formulas, and see SohCahToa examples that show how to solve right triangle problems. Relation in Math: Definition & Examples

In this lesson, you will learn the definition of relation in terms of mathematics, as well as the various ways of displaying relations. We will also look at some examples. Mathematical expressions that contain a radical symbol (√) are called radical expressions. Learn how to define radical expressions, the history of the term radical, how to use examples to solve radical equations, and special circumstances when radical expressions have no real roots.

### Step  1  :

#### Trying to factor by splitting the middle term

1.1     Factoring  x2-4x-2

The first term is,  x2  its coefficient is  1 .
The middle term is,  -4x  its coefficient is  -4 .
The last term, "the constant", is  -2

Step-1 : Multiply the coefficient of the first term by the constant   1 • -2 = -2

Step-2 : Find two factors of  -2  whose sum equals the coefficient of the middle term, which is   -4 .

 -2 + 1 = -1 -1 + 2 = 1

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

x2 - 4x - 2 = 0

### Step  2  :

#### Parabola, Finding the Vertex :

2.1      Find the Vertex of   y = x2-4x-2

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   2.0000

Plugging into the parabola formula   2.0000  for  x  we can calculate the  y -coordinate :
y = 1.0 * 2.00 * 2.00 - 4.0 * 2.00 - 2.0
or   y = -6.000

#### Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-4x-2
Axis of Symmetry (dashed)  {x}={ 2.00}
Vertex at  {x,y} = { 2.00,-6.00}
x -Intercepts (Roots) :
Root 1 at  {x,y} = {-0.45, 0.00}
Root 2 at  {x,y} = { 4.45, 0.00}

#### Solve Quadratic Equation by Completing The Square

2.2     Solving   x2-4x-2 = 0 by Completing The Square .

Add  2  to both side of the equation :
x2-4x = 2

Now the clever bit: Take the coefficient of  x , which is  4 , divide by two, giving  2 , and finally square it giving  4

Add  4  to both sides of the equation :
On the right hand side we have :
2  +  4    or,  (2/1)+(4/1)
The common denominator of the two fractions is  1   Adding  (2/1)+(4/1)  gives  6/1
So adding to both sides we finally get :
x2-4x+4 = 6

Adding  4  has completed the left hand side into a perfect square :
x2-4x+4  =
(x-2) • (x-2)  =
(x-2)2
Things which are equal to the same thing are also equal to one another. Since
x2-4x+4 = 6 and
x2-4x+4 = (x-2)2
then, according to the law of transitivity,
(x-2)2 = 6

We'll refer to this Equation as  Eq. #2.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of
(x-2)2  is
(x-2)2/2 =
(x-2)1 =
x-2

Now, applying the Square Root Principle to  Eq. #2.2.1  we get:
x-2 = √ 6

Add  2  to both sides to obtain:
x = 2 + √ 6

Since a square root has two values, one positive and the other negative
x2 - 4x - 2 = 0
has two solutions:
x = 2 + √ 6
or
x = 2 - √ 6

2.3     Solving    x2-4x-2 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

- B  ±  √ B2-4AC
x =   ————————
2A

In our case,  A   =     1
B   =    -4
C   =   -2

Accordingly,  B2  -  4AC   =
16 - (-8) =
24

4 ± √ 24
x  =    —————
2

Can  √ 24 be simplified ?

Yes!   The prime factorization of  24   is
2•2•2•3
To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 24   =  √ 2•2•2•3   =
±  2 • √ 6

√ 6   , rounded to 4 decimal digits, is   2.4495
So now we are looking at:
x  =  ( 4 ± 2 •  2.449 ) / 2

Two real solutions:

x =(4+√24)/2=2+√ 6 = 4.449

or:

x =(4-√24)/2=2-√ 6 = -0.449

### Two solutions were found :

1.  x =(4-√24)/2=2-√ 6 = -0.449
2.  x =(4+√24)/2=2+√ 6 = 4.449
Sours: https://www.tiger-algebra.com/drill/x~2-4x-2=0/
x^2+4x-32=0

## Linear equations with one unknown

### Step  2  :

#### Pulling out like terms :

2.1     Pull out like factors :

x2 - 4x  =   x • (x - 4)

x • (x - 4) = 0

### Step  3  :

#### Theory - Roots of a product :

3.1    A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

#### Solving a Single Variable Equation :

3.2      Solve  :    x = 0

Solution is  x = 0

#### Solving a Single Variable Equation :

3.3      Solve  :    x-4 = 0

Add  4  to both sides of the equation :
x = 4

### Two solutions were found :

1.  x = 4
2.  x = 0
Sours: https://www.tiger-algebra.com/drill/x~2-4x=0/

## 4x solve 2

.

Quadratic Equation: Solve 4x^2 + 2x = 0

.

### You will also like:

.

1286 1287 1288 1289 1290