Sunday, August 2, 2015

Verify if the inequality is true. Discuss! 2x^2 + 5x

First, we have to subtract 12, both sides of the equation
(it's easier to verify if an expression is negative or
positive).


2x^2 + 5x - 12 <
0


Now, it would be much more easier to factorize the
expression. In order to do so, we'll find out the roots of the equation 2x^2 + 5x - 12 =
0


x1 = [-5+sqrt(25+96)]/4


x1 =
(-5+11)/4


x1 = 6/4


x1 =
3/2


x2 = (-5-11)/4


x2 =
-16/4


x2 = -4


Now, we'll
factorize the expression 2x^2 + 5x - 12:


2x^2 + 5x - 12 =
2(x+4)(x-3/2)


2x^2 + 5x - 12 =
(x+4)(2x-3)


Now, we'll discuss when
(x+4)(2x-3)<0.


For a product to be negative, the
factors of the product have to have opposite signs. From here, it results 2
cases:


First
case:


x+4>0 and
2x-3<0


x>-4 and
x<3/2


x belongs to the interval
(-4,3/2).


Second
case:


x+4<0 and
2x-3>0


x<-4 and
x>3/2


It is obvious that there are no real numbers
to satisfy this condition,
simultaneously.


So, the inequality is
verified for x belongs to the interval (-4,3/2).

No comments:

Post a Comment

In Act III, scene 2, why may the establishment of Claudius&#39;s guilt be considered the crisis of the revenge plot?

The crisis of a drama usually proceeds and leads to the climax.  In Shakespeare's Hamlet , the proof that Claudius is guilty...