For what values of m does the graph of y = 3x^2 + 7x + m have two x-intercepts? a) m>12/49 b) m<12/49 c) m 49/12

The quadratic formula, has a part we call the "discriminant" defined by the variables that are inside the square root, and is denotated by "delta":

Δ = b2 - 4ac Whenever we solve a quadratic equation that is complete and we analyze the discriminant, we can get 3 scenarios: if→Δ>0 = > ∃ x1, x2 / a x2 + bx+c=0 This just means: "if the discriminant is greater than zero, there will exist two x-intercepts" And for the second scenario: if→Δ=0→∃ xo / a x2 + bx+c=0 This means: "if the discriminant is equal to zero, there will be one and only one x-intercept" And for the last scenario: if→Δ<0→∃x∉R/a x2 + bx+c=0 This means that : "if the discriminant is less than zero, there will be no x-intercepts" So, if we take your excercise and analyze the the discriminant: 3 x2 + 7x+m=y we will find the values that satisfy y=0 : 3 x2 + 7x+m=0 And we'll analyze the discriminant: Δ = 72 - 4 (3) (m) And we are only interested in the values that make the discriminant equal zero: 72 - 4 (3) (m) = 0 All you have to do is solve for "m".