Question

How do you solve and write the following in interval notation: `x^2 -3x -10 >0`?

Answer 1

`(-oo,-2)uu(5,+oo)`

Explanation:

`"factorise the left side"`

`rArr(x-5)(x+2)>0`

`"the zeros are " x=5" and "x=-2`

`"these indicate where the function may change sign"`
`"and 'splits the x-axis into 3 intervals, namely"`

`x<-2,color(white)(x)-2 < x <5,color(white)(x)x>5`

`"consider a "color(blue)" test point ""in each interval"`

`"substitute each test point into the function and consider "`
`"it's sign"`

`x=-5to(-)(-)tocolor(red)" positive"`

`x=1to(-)(+)tocolor(blue)" negative"`

`x=6to(+)(+)tocolor(red)" positive"`

`"we want to find where the function is positive ">0`

`"this occurs when "x<-2" or " x>5`

`rArr(-oo,-2)uu(5,+oo)larr" interval notation"`
graph{x^2-3x-10 [-10, 10, -5, 5]}