To find a value of b for which the equation x^4 + bx^3 + 1 = 0 has no real root, we need to consider the discriminant of the equation. The discriminant is given by the expression b^2 - 4ac, where a = 1, b = b, and c = 1.

The discriminant determines the nature of the roots of a quadratic equation. If the discriminant is positive, the equation has two distinct real roots. If the discriminant is zero, the equation has one real root (a double root). And if the discriminant is negative, the equation has no real roots.

In this case, we have a quartic equation, but we can still use the discriminant to determine the nature of the roots. By comparing the quartic equation to a quadratic equation, we can see that the discriminant is given by b^2 - 4(1)(1) = b^2 - 4.

Since we want the equation to have no real roots, we need the discriminant to be negative. Therefore, we need b^2 - 4 < />

Solving this inequality, we have:

b^2 - 4 < />
b^2 < />
|b| < />

This means that the value of b must lie between -2 and 2 for the equation to have no real roots.

Now let's consider the answer choices:

(a) 11/5: This value is greater than 2, so it does not satisfy the condition.

(b) -3/2: This value lies between -2 and 2, so it satisfies the condition.

(c) 2: This value is equal to 2, so it does not satisfy the condition.

(d) 5/2: This value is greater than 2, so it does not satisfy the condition.

Therefore, the possible value of b that satisfies the condition is -3/2.