The graph of a quadratic equation y = ax^2 + bx + 1 passes through the point (1, 2). For what values of a does the graph of y intersect the x − axis at two distinct points?

Lines p and q intersect. find the value of b. show your work. cite any theorems you use.

Nine more than four times a number is the same as one less than twice the number. find the number?

The probability that a student graduating from suburban state university has student loans to pay off after graduation is .60. if two students are randomly selected from this university, what is the probability that neither of them has student loans to pay off after graduation?