Thread: Inequality with higher degree

x^4-x<0

How do I solve it?

Have you tried to factor the LHS yet?

I tried doing X(X^3 -1) <0 then x=0 x^3-1=0 didn't work when i checked using solution

Maybe you can factor further?

Hint:

Sketching the graph of will help after you have found the zeros.

Originally Posted by RK29

x^4-x<0 How do I solve it?

Can you see that
So can you solve
If so solve it.

Originally Posted by RK29

I tried doing X(X^3 -1) <0 then x=0 x^3-1=0 didn't work when i checked using solution

Hint: f(1)=0 and so (x-1) is a factor.

Originally Posted by RK29

x^4-x<0

How do I solve it?

is non-negative number for all

So when, ?

x must be positive, but not greater than . Can you see that?

Originally Posted by RK29

x^4-x<0

How do I solve it?

note that the factor for all x (how can you check that the factor is always positive?)

for the other two factors that can equal zero ... critical values are x = 0 and x = 1

these two critical values divide the x-value number line into three regions ...

x < 0 , 0 < x < 1 , and x > 0

test a single x-value from each of the above intervals into the original inequality to see if this value makes the inequality true or false ...

if true, then all values of x in that interval make the inequality true ... if false, then otherwise.

This works as well just remember to put the strict inequity back in the answer.