Answer:
[tex]\large\boxed{m<\dfrac{49}{12}}[/tex]
Step-by-step explanation:
x-intercepts are for y = 0.
Put y = 0 to the equation y = 3x² + 7x + m.
Calculate the discriminant of quadratic equation ax² + bx + c = 0:
Δ = b² - 4ac
if Δ < 0, then an equation has no solution
if Δ = 0, then an equation has one solution
if Δ > 0, then an equation has two solution.
a = 3, b = 7, c = m
Δ = 7² - 4(3)(m) = 49 - 12m
Two x-intercepts for Δ > 0.
Solve the inequality:
[tex]49-12m>0[/tex] subtract 49 from both sides
[tex]-12m>-49[/tex] change the signs
[tex]12m<49[/tex] divide both sides by 12
[tex]m<\dfrac{49}{12}[/tex]
