Question

Solve 2x^2 + 5x -3 ≤ 0

A. {-1 ≤ x ≤ 3/2}
B. { -1/2 ≤ x ≤ 3}
C. { -3 ≤ x ≤ 1/2}

Please show work !

Answer 1

Hello from MrBillDoesMath!

Answer: 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