Question #5984e

3 Answers
Nov 30, 2017

(x+4)(2x-3) <= 0

Explanation:

We are given the quadratic inequality

2x^2 + 5x - 12 <= 0

Split the middle term as shown below:

2x^2 + 8x - 3x - 12 <= 0

2x(x+4) - 3(x+4) <= 0

Hence, we can conclude that

(2x - 3) (x + 4) <=0

is what we get after factorizing the given quadratic inequality.

Nov 30, 2017

x<=3/2 and x<=-4

Explanation:

.

2x^2+5x-12<=0

Let's add and subtract 3x to the equation:

2x^2+3x-3x+5x-12<=0

2x^2-3x+8x-12<=0

x(2x-3)+4(2x-3)<=0

(2x-3)(x+4)<=0

2x-3<=0 This gives us x<=3/2

x+4<=0 This gives us x<=-4

Solution includes all of (-4,3/2)

Nov 30, 2017

Please see below.

Explanation:

2x^2+5x-12 = 0 when

(2x-3)(x+4)=0 which happens at

x=3/2 and at x=-4

These numbers partition the number line into the intervals:

(-oo,-4) " " (-4,3/2) " " (3/2,oo)

Pick a number in each interval and test the inequality.

I'll use -10, 0 and 10

At x = -10, we have
(2x-3)(x+4)=(2(-10)-3)((-10)+4) which is a negative times a negative, so it is positive and the inequality is false.

At x = 0, we have
(2x-3)(x+4)=(2(0)-3)((0)+4) which is a negative times a positive, so it is negative and the inequality is true.
The solutions include all of (-4,3/2).

At x = 10, we have
(2x-3)(x+4)=(2(10)-3)((10)+4) which is a positive times a positive, so it is positive and the inequality is false.

The solution set is

(-4,3/2).