Solve give your answer in interval notation: 5-4x^2> =!! : ( on the answer key for my final study guide it says that the answer is [-5,1/2] but on the calculator it says that the answer is [-5/2,1/2] i want to know which of these answers is ! : )

[-5/2, 1/2] is the correct answer

Step-by-step 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]

_____

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.

step 2

Step-by-step explanation: