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 x^2 -4x < 0

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hadeelhadool | Student, Grade 11 | eNoter

Posted July 6, 2010 at 9:44 AM via web

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 x^2 -4x < 0

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3 Answers | Add Yours

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neela | High School Teacher | Valedictorian

Posted July 6, 2010 at 9:54 AM (Answer #1)

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To solve x^2-4x < 0.

X^2-4x < x(x-4) . So the given equation is

x(x-4) < 0.

x=0, x-4 = 0  are the roots.

Therefore as long x  x belongs to (0, 4), the expression x and (x-4) have opposite signs. Therefore the product x(x-4) is negative for x in (0,4). Or ) < x <4 for which x(x-4) or x^2-4x < 0.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted July 6, 2010 at 9:50 AM (Answer #2)

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x^2 -4x < 0

Let us factor x :

x(x-4) <0

Then we have two options:

option 1:

x < 0    and x-4>0

x<0     and x > 4

This is impossible solution because x can not be < 0 and > 4 at the same time.

Option 2:

x> 0  and  x-4 < 0

x>0   and x<4

Then x belongs to the interval (0,4) .......(2)

Then, from (1) and (2) we conclude that:

X belongs to (0,4)

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giorgiana1976 | College Teacher | Valedictorian

Posted July 6, 2010 at 3:58 PM (Answer #3)

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First of all, let's solve the expression like an equation. For this reason, we'll put:

x^2 -4x = 0

We'll factorize and we'll get:

x(x-4) = 0

We'll put each factor equal to zero.

x = 0

x-4 = 0

x = 4

Now, we'll follow the rule: between the solution of the equation, the expression will have the opposite sign of the coefficient of x^2, that means that x(x-4)<0, outside the solutions, the expression will be positive.

So, the conclusion is that the expression is negative for values of x which are in the interval (0,4).

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