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

The graph of has two x-intercepts when m < 49/12

The given equation is:

The equation  will have two intercepts if:

To find the value of x, use the equation

In the equation :

a = 3,  b = 7, c = m

x  =  -b/2a

x  = -7/2(3)

x  =  -7/6

Substitute x = -7/6 into

The graph of has two x-intercepts when m < 49/12

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We want to find for which values of m the given equation has two x-intercepts.

We must have m < 4.083

A general quadratic equation is:

a*x^2 + b*x + c

To study the roots, we need to study the determinant.

D = b^2 - 4*a*c

So if we want two x-intercepts, we must have D > 0.

Our equation is:

y = 3*x^2 + 7*x + m

The determinant is:

D = (7)^2 - 4*3*m > 0

49 - 12*m > 0  

49 > 12*m

49/12 > m

4.083 > m

So if we want to have two x-intercepts, we must have m < 4.083

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