Math
posted by Ashley .
Please please help!!!!!
Solve the inequality and write the solution set in interval notation
4x^3 6x^2<0
2x^2 (2x3)<0
2x3<0
x= 3/2
Now I'm not sure about this
2x^2<0
x^2<1/2
sq root of x^2<sq root of 1/2
x=.7071
Right?
When I plug it in the calculator it says
X=0
How?

4x^3  6x^2 < 0
2x^2 (2x3) < 0
You should know the general shape of this graph. It has a double root at x=0 and it crosses the xaxis at x=3/2.
So, the graph is below the xaxis for all values of x less than 3/2, except x=0.
2x3 < 0 is an inequality.
You cannot change it to an equation: x = 3/2
2x3 < 0
2x < 3
x < 3/2

If 2x^2 < 0
you cannot say x^2 < 1/2
0/2 = 0
HINT: x^2 is always >=0, so 2x^2 is always >= 0.
Always
(a) check your answer in the original expression
(b) THINK about your answer in the context of the problem!