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

Question

i need the answer to my question

 

Answer 1

The graph is a parabola with the minimum where x= -b/2a = -7/6.  You should sketch it!

To have 2 x intercepts, the value at the minimum point must be less than 0, i.e.

3(49/36) - 49/6 + m < 0

49/12 - 49/6 + m < 0

(49-98)/12 + m < 0

-49/12 + m < 0

m < 49/12

Answer 2

The discriminant of Ax² + Bx + C is B² - 4AC

 

   If y = Ax² + Bx + C, then there are:

 

      2 x-intercepts if the discriminant is positive

 

      1 x-intercept if the discriminant is zero

 

      no x-intercepts if the discriminant is negative

 

So, for y = 3x² + 7x + m, B² - 4AC = 49 - 12m

 

       49 - 12m > 0

 

           - 12m > -49

 

                 m < 49/12