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Answer:
-1/2 < x < 3
Explanation:
First you need to find the x-intercepts. Since the leading coefficient is positive, you know the graph is decreasing through the left x-intercept, so will be negative between the x-intercept values.
f(x) = 2x^2 -5x -3
f(x) = 2x^2 -6x +x -3
f(x) = 2x(x -3) +1(x -3)
f(x) = (2x +1)(x -3)
The x-intercepts are the values of x that make these factors zero:
2x +1 = 0 ⇒ x = -1/2
x -3 = 0 ⇒ x = 3
The graph of f(x) is negative on the interval ...
-1/2 < x < 3