Answer:
Description
Step-by-step explanation:
1. Factor 2x^2+11x+12 -> (2x+3)(x+4)
x=-4, -3/2
Both numbers are rational numbers as both can be expressed in the form in a quotient with integer values.
2. If discriminant is negative, then solutions are imaginary, meaning that the discriminant is less than 0, so you can set up this equation.
11^2 - 4(a)(12) < 0
121 - 48a < 0
a>121/48
The closest integer to 121/48 (~2.52) such that it satisfies the above conditions is 3, so the lowest value for a is 3.
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