Answer:
[tex]m<49/12[/tex]
Step-by-step explanation:
we are given
[tex]y = 3x^2+7x+m[/tex]
To find x-intercept means we have to find zeros
and for finding zeros , we will use quadratic formula
and we have it has two x-intercepts
so, it's discriminant must be greater than 0
so, we will find discriminant
[tex]D = \sqrt{b^2-4ac}[/tex]
now, we can compare with
[tex]y=ax^2+bx+c\\y=3x^2+7x+m[/tex]
and then we can find a , b and c
a = 3, b = 7, c = m
now, we can find D
[tex]D = \sqrt{7^2-4*3*m} \\D=\sqrt{49-12m}[/tex]
It has two x-intercepts
so,
[tex]D = \sqrt{49-12m}>0[/tex]
now, we can solve for m
[tex]49-12m>0\\12m<49\\m<49/12[/tex]
