Question

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.

Answer 1

`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