Answer:Step-by-step explanation:One way to approach this problem is to apply the quadratic formula to each of the four given possible answers and see whether any of them match the given roots. The other way is to work backwards from the given roots to determine the original quadratic equation.First, let's find the roots of the first possible equation, x^2 + 4x + 49 = 0. Here, a = 1, b = 4 and c = 49, and so the roots are -4 ± √(16 - 4[1][49] )x = -------------------------------- 2(1)We must reject this possible answer immediately because the quantity under the radical sign is negative, which would lead to complex roots. The given roots are not complex; they are real.Next, let's find the roots of the first possible equation, x^2 - 4x - 49 = 0. Here, a = 1, b = -4 and c = -49, and the roots are: 4 ± √ (16 - 4[1][-49] ) 4 ± √ 212x = --------------------------------- = -------------------- 2(1) 2We must reject this possible answer because the quantity (212) under the radical does not simplify to the 3√5 that appears in the given roots.Reject the third possible answer for the same reason that we reject the first one (see explanation, above).Determine the roots of the fourth possible answer choice: -4 ± √ (16 - [4][1][-41] ) -4 ± √ 184 -4 ± √4 √6 x = ---------------------------------- = ----------------- = -------------------- = -2 ± √6 2 2 2These results do not match the given roots.Unfortunately, none of the given possible answer choices yields solutions matching the given roots.