SOLUTION: If f(x)=x(x+3)(x-1), use interval notation to give all values of x where f(x)>0. Thanks for your time.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If f(x)=x(x+3)(x-1), use interval notation to give all values of x where f(x)>0. Thanks for your time.      Log On


   

Question 44533This question is from textbook
: If f(x)=x(x+3)(x-1), use interval notation to give all values of x where f(x)>0.
Thanks for your time. This question is from textbook

Found 2 solutions by venugopalramana, Nate:
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
If f(x)=x(x+3)(x-1), use interval notation to give all values of x where f(x)>0.
THE ROOTS ARE 0,-3,1.....-3,0,1 IN INCREASING ORDER
PLACE THE ROOTS ON A NUMBER LINE AS SHOWN BELOW
....<-3.......-3...........0........1.......>1....IN INCREASING ORDER.
NOW COME FROM RIGHT MOST
ZONE 1.....>1...THAT IS BEYOND THE LARGEST ROOT ..F(X) WILL BE +VE
ZONE 2.....BETWEEN 0 AND 1.........................F(X) WILL BE -VE
ZONE 3.....BETWEEN -3 AND 1..................... ..F(X) WILL BE +VE
ZONE 4.....<-3.....................................F(X) WILL BE -VE
HENCE F(X)>0 IN INTERVALS
X>1 THAT IS (1,INFINITY) AND -3

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x(x+3)(x-1)
Look at this ---->
0 < x(x + 3)(x - 1)
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3+%2B+2x%5E2+-+3x+%29+
Answer: (-3,0) and (1,+infinity)