Hi. I've been attempting this modulus problem from my textbook for the past hour and could not find a way to get the correct answer. 1. The problem statement, all variables and given/known data The equation x^2 -(k+2)x + 2k + 1 = 0 ,where k is a constant has two real roots α and β. 1)Express α+β and αβ in terms of k b) if |α| = |β| , find 2)the possible values of k 3)the roots corresponding to each value of k 2. Relevant equations α+β = -b/a αβ = c/a b^2-4ac = 0 / D = 0 or >/< or >= / =< 3. The attempt at a solution Part 1 is just formula,no problem with that. 2)I presumed from the question that since the equation has two real roots(cuts at two distinct points) and/or since the modulus of alpha is equal to the modulus of beta,the roots may also be the same and therefore i applied the formula b^2 -4ac ≥ 0 (-(k+2))^2 - 4(1)(2k+1) ≥ 0 k^2-4k ≥ 0 k(k-4)≥0 By solving using quadratic inequalities, k ≥ 4 or k ≤ 0 I referred to the answer for the possible values of k and it was 4,0,-2 . If i did a guess and check by substituting k = 4 into the equation i will get the same roots when they are in modulus form and this is also true for k = 0 . I guess this method although gives me the correct answer and proves it ,is wrong. This is because I cannot find the other possible value of k which was -2 unless i did a guess and check by going under 0 as shown in the inequality but I guess that there must be another method(as i presume that doing guess and check can yield an infinite number of solutions with decimal places etc.) . I need help on that. Any inputs is kindly appreciated.