Final answer:
The correct equation with the roots 3±2√2 is x²−6x+7=0, found by matching the roots to the quadratic formula's discriminant and the value of 'b'. Therefore, D is the correct equation with roots 3±2√2.
Step-by-step explanation:
The given roots are 3±2√2. To determine which equation has these roots, we can use the quadratic formula, -b ± √b² - 4ac over 2a. Applying this formula to each option and comparing the results with the given roots will help us identify the correct equation.
When we apply the quadratic formula to the equation form ax²+bx+c = 0, the roots are given by the expression -b ± √b² - 4ac over 2a. The solutions will match the given roots if the discriminant (b² - 4ac) is equal to (2√2)² = 8 and if the coefficient of 'x' (the value of 'b') is -6.
Option D, x²−6x+7=0, has 'b' as -6, and its discriminant is (-6)² - 4(1)(7) = 36 - 28 = 8, which matches the square of the given root's non-rational part. Therefore, D is the correct equation with roots 3±2√2.