# Regarding the factor and remainder theorem?

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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.

The polynomial

(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

#### Explanation:

We know that the function can be written

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

When x= 0 the function is positive

Therefore it is negative if

Hope this helps