Question

How do you solve and write the following in interval notation: `x^2 + 15x > -50`?

Answer 1

`x< -10 or x> -5`

Explanation:

`x^2+15x > -50 iff x^2+15x+50>0`

Let `f(x)=x^2+15x+50=(x+5)(x+10)`

We can easily see that if `f(x)=0 => x=-5 or x=-10`
We can also see that 'a' is positive (the form of `y=ax^2+bx+c`)

This is the x axis:

---------------------0------------------>x

We put the (-5,0) and (-10,0):

---------(-10)---------(-5)-----------0-------->x

'a' is positive, (`color(red)(+)x^2+15x+50`), so it is a "smiling parabola":

`color(blue)(---)(-10)---(-5)color(blue)(---0--->)`x

So the answer is `x< -10 or x> -5`