Nature of Roots of a Cubic Polynomial Using Derivatives

Q. Which of the following could be the possible integral value(s) of 'a' for which the equation $x^3-3x+a=0$ has three distinct roots?

1. 1
2. -1
3. \N
4. 3
5. -3

Q. The roots of the equation $x^3$ + 2$x^2$ + 5x + 2cos x = 0 in [0, 2$\pi$] is

1. only one root
2. only two roots
3. only three roots
4. NO ROOTS EXIST

Q. The roots of the equation $x^3$ + 2$x^2$ + 5x + 2cos x = 0 in [0, 2$\pi$] is

1. only one root
2. only two roots
3. only three roots
4. NO ROOTS EXIST