Final answer:
The correct answer is option c. The polynomial expression -12x^2 - 25x + 5x^3 has 3 roots because it is a cubic polynomial, and by the Fundamental Theorem of Algebra, a polynomial of degree 3 will always have 3 roots.
Step-by-step explanation:
In the polynomial expression -12x2 - 25x + 5x3, the number of roots is determined by the highest power of x, which is the degree of the polynomial. Since we have a cubic term (5x3), the polynomial is of degree 3. According to the Fundamental Theorem of Algebra, a polynomial of degree n will have exactly n roots, although some roots may be complex or repeated. Therefore, the polynomial in question will have 3 roots.
When we reorganize the polynomial to 5x3 - 12x2 - 25x, it's easier to see the highest degree as the first term. No matter the coefficients and whether all roots are real or not, a cubic polynomial will always have three roots according to the theorem.
Hence, the correct option for this question is:
c) 3