Problema Solution
Solve the inequality. Be sure to show all of your work and show your final answer using interval notation.
f (x)=2x^2+3x-9
Answer provided by our tutors
f(x)=2x2+3x-9
=2x2+6x-3x-9
=2x(x+3)-3(x+3)
=(x+3)(2x-3)
case 1 f(x)=0
(x+3)(2x-3)=0
x=-3,3/2
case 2 f(x)>0
(x+3)(2x-3)>0
x>-3and x>3/2
or x<3 and x>3/2
case 3 f(x)<0
(x+3)(2x-3)<0
x<-3 andX>3/2
X>3 and >3/2