Final answer:
The function f(x)=(x+3)(2x-1)^2 has a total of 3 roots, one at x = -3 and a double root at x = 0.5.
Step-by-step explanation:
To determine how many roots the function f(x)=(x+3)(2x-1)^2 has, we need to analyze the factors and their powers. A root occurs when a function equals zero. The term (x+3) indicates a root at x = -3, because that's when the factor equals zero. The term (2x-1)^2 indicates a single root at x = 0.5 (or x=1/2), but since this term is squared, it actually touches the x-axis at this point but does not cross it. This is often referred to as a repeated or double root.
Therefore, the function has one distinct root at x = -3 and a double root at x = 0.5. In total, there are 3 roots (if the repeated root is counted separately), making the correct answer 'd'.