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

1 Answer
Dec 26, 2017

Answer:

#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#