Find the values of p for which the equation `x^(4)-14x^(2)+24x-3-p=0` has
(a) Two distinct negative real roots
(b) Two real roots of opposite sign
(c) Four distinct real roots
(d) No real roots

Explanation

To solve the equation \( x^4 - 14x^2 + 24x - 3 - p = 0 \) for the different conditions regarding the values of \( p \), we will analyze the function \( f(x) = x^4 - 14x^2 + 24x - 3 \).

### Step 1: Find the critical points of \( f(x) \)

To find the critical points, we differentiate \( f(x) \):

\[
f'(x) = 4x^3 - 28x + 24
...