Question

Describe the solution set of each of the following quadratic inequality or not​

Answer 1

See below

All the inequalities can be solved by making a table, but once they are simple factored quadratic expressions, we already know what interval it will have.

Explanation:

1)

`x^2+9x+14>0`

Factoring the expression, we have

`(x+2)(x+7)>0`

Considering that

`(x+2)(x+7)=0`

for
`x = -2` and
`x=-7` you can see that for

`(x+2)(x+7)>0`

`x \\ot\in (-7, -2)`

Therefore,

`S = \{x\in\mathbb{R} : x<-7 \text{ or } x>-2 \}`

`S = (-\infty,-7)\cup (-2,\infty)`

2)

`x^2-10x+16<0`

You can factor it again.

`(x-2)(x-8)<0`

You can make the table to solve all the inequalities, but once we have the expression
`< 0`, we know that

`2<x<8`, therefore,

`S = (2, 8)`

3)

`2x^2+11x+12<0`

Factoring we have

`(2x+3)(x+4)<0`

Find the solutions for

`(2x+3)(x+4)=0`

And we know that

`-4<x<-(3)/(2)`

`S = \left(-4,-(3)/(2)\right)`