Final answer:
The quadratic equation with roots 9-4i and 9+4i is x² - 18x + 97 = 0, because the sum of the roots is 18 and the product is 97.
Step-by-step explanation:
The student is looking for a quadratic equation with given complex roots. To find an equation with roots 9-4i and 9+4i, we can use the property that the sum and product of the roots can lead us to 'b' and 'c' in the quadratic equation of the form ax²+bx+c = 0. Since the sum of the roots (s) is (9-4i)+(9+4i)=18 and the product of the roots (p) is (9-4i)(9+4i)=97, we can construct the equation x² - sx + p = 0, which becomes x² - 18x + 97 = 0. Thus, the correct answer is a) x² - 18x + 97 = 0.