Solve 2x^2 + 5x -3 ≤ 0 a. {-1 ≤ x ≤ 3/2} b. { -1/2 ≤ x ≤ 3} c. { -3 ≤ x ≤ 1/2} show work !

Hello from MrBillDoesMath!

 Choice C

Discussion:

Let's looks at things one case at a time:

A. The value 1 lies in set A but 2x^2 + 5x -3 at x = 1,  = 2(1)^2 + 5*1  -3 =4 which is NOT <=0

B.  As in choice A, the value x = 1 lies in set B but does not does not yield  2x^2 + 5x -3 <= 0

So C is the only remaining option.

Alternate approach.

Factor the polynomial:

2x^2 + 5x -3 = (2x-1) (x + 3)

so for 2x^2 + 5x -3 <= 0

one of the factors must be positive and the other negative. Do the analysis and you will get choice C as the answer

Thank you,

MrB

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step-by-step explanation: