Regarding the factor and remainder theorem?

The polynomial #4x^3-4x^2+3x+a#, where a is a constant, is denoted by p(x). It is given that p(x) is divisible by #2x^2-3x+3#.
(i) Find the value of a. (I'm done with this part of the question. The value of a is 3. It's the second part that's troubling me.)
(ii) When a has this value, solve the inequality p(x) < 0, justifying your answer.

1 Answer
Aug 24, 2016

Answer:

#x<-1/2#

Explanation:

We know that the function can be written #(2x^2-3x+3)(2x+1)#
What does the graph look like?
The determinant of the quadratic part indicates no real solution so the graph only crosses the X axis at #x=-1/2#
When x= 0 the function is positive
Therefore it is negative if #x<-1/2#
Hope this helps