For what values of m does the graph of y = 3x2 + 7x + m have two x-intercepts?

A. M>25/3

B. M<25/3

C. M<49/12

D. M>49/12

The definition tells us that the graph of a function f has one or more x - intercepts if and only if 0=f (x). We have, y = 3x2 + 7x + m for finding the value of x-intercept, we equalize y to 0, that means y = 3x2 + 7x + m=0, or y = 3x2 + 6x + m=0. 3x2 + 7x + m=0 has two different zeros if 7² - 4 x3 x m >0, and we know that 49 - 12m>0 implies - 12m > - 49, multiplying by - 1 the two members of the inequality, we get 12m<49, and it is equivalent to m<49/12, the true answer is C