Solve the inequality and select the solution set in interval notation: 2x2 + 3x + 2 > 0?

Question

A. (-∞, -1/2)
B. (-∞, 1)
C. (2, ∞)
D. Any real numbers

Answer 1

Assuming you mean 2x^2 + 3x + 2 > 0, this problem has only complex number roots (because the discriminant b^2-4ac is -7). That means the function is positive for all real numbers ... so the answer is "D".

In similar expressions that aren't "any real number", what you'd do is factor the expression. You'd then take the opposites of the factors to find the roots, which will divide the real numbers into three parts. Use the rules of negative numbers (neg X pos = neg; neg X neg = pos, etc.) to determine in which of those intervals (usually either the middle one or the two outside ones) the answer is positive.