Question

For what values of m does the graph of y = 3x2 + 7x + m have two x-intercepts?
m greater-than StartFraction 25 Over 3 EndFraction
m less-than StartFraction 25 Over 3 EndFraction
m less-than StartFraction 49 Over 12 EndFraction
m greater-than StartFraction 49 Over 12 EndFraction

Answer 1

The quadratic has two x-intercepts when its discriminant is positive:
D = b^2 − 4ac = 7^2 − 4(3)(m) = 49 − 12m > 0.
So 12m < 49 ⇒ m < 49/12.
Thus the correct choice is: m less-than 49/12.