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

1 Answer
Jul 14, 2017

Answer:

#(-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]}