Question

For what real numbers x is 3x^2+5x-2 positive?
a) (-2, 1/3)
b) (-∞,-2) and (1/3, ∞)
c) (-∞,-2)
d) (-∞,1/3) and (-2,∞)
Answer is b
Please explain how to get to this answer, thank you

Answer 1

Okay let's begin by translating the problem into a mathematical language, we want the values of x that makes the whole equation into a positive one, si that means we want the x to be equal or greater than zero. (You might want it just greater for better answer).
So what we want is this:
\[3x^2 +5x-2 > 0\]
All we have to do now is factor that quadratic equation on the left side to see what values of x actually gives us 0.
Can you factor it?

Answer 2

that would be (3x-1)(x+2) so x=1/3 and x=-2