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1 solution
Write :
Inq1 : x 2 + m x + n < 0
Inq2 : x 2 + 4 x ≥ 0
The solution of Inq2 is − 4 ≤ x ≤ 0 . Since the solution of both inequality is 0 < x < 6 , then the roots of equation x 2 + m x + n = 0 are 6 and − 4 < α < 0 , so both m and n are negative. Hence we have, m + n = − 1 1 6 m + n = − 3 6
Then, m = − 5 and n = − 6 . So, we have m n = 3 0 .