Answer:
[-5/2, 1/2] is the correct answer
Explanation:
Subtract the left side to compare to zero:
... 4x^2 +8x -5 ≤ 0
... (2x +5)(2x -1) ≤ 0 . . . . factor
... x = -5/2 . . . or . . . x = 1/2 . . . . are the zeros
The factors will differ in sign (the product will be negative) when x is between the zero values. Hence the solution set is ...
... x ∈ [-5/2, 1/2]
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Check
When you normalize the leading coefficient of the quadratic to 1, it becomes ...
... x² +2x -5/4 ≤ 0
Now, you know the sum of zeros must be -2 and the product of zeros must be -5/4. The zeros associated with the answer given in your key have a sum of -4.5 and a product of -5/2. It cannot be right.