Final answer:
To find the complete factored form of the polynomial f(x) = 2x^2 - 19x + 42 with zeros 7/2 and 6, we create factors from the zeros, resulting in f(x) = 2(x - 6)(2x - 7).
Step-by-step explanation:
To use the given zeros to write the complete factored form of f(x), we can create factors from each zero. The zeros of the quadratic polynomial f(x) = 2x2 - 19x + 42 are 7/2 and 6. Therefore, we can create factors based on these zeros.
For the zero 7/2, the corresponding factor is (2x - 7), because when 2x is equal to 7, x is equal to 7/2. Similarly, for the zero 6, the corresponding factor is (x - 6), because when x is equal to 6, the value of the function is zero.
Now, we combine these two factors and multiply them by the leading coefficient of the given quadratic, which is 2. Thus, the complete factored form of f(x) is:
f(x) = 2(x - 6)(2x - 7)