The graph of [tex]y = 3x^2+7x+m[/tex] has two x-intercepts when m < 49/12
The given equation is:
[tex]y = 3x^2+7x+m[/tex]
The equation [tex]y = 3x^2+7x+m[/tex] will have two intercepts if:
[tex]3x^2+7x+m < 0\\\\[/tex]
To find the value of x, use the equation [tex]x = \frac{-b}{2a}[/tex]
In the equation [tex]y = 3x^2+7x+m[/tex]:
a = 3, b = 7, c = m
x = -b/2a
x = -7/2(3)
x = -7/6
Substitute x = -7/6 into [tex]3x^2+7x+m < 0\\\\[/tex]
[tex]3(\frac{-7}{6})^2+7(\frac{-7}{6} )+m<0\\\\3(\frac{49}{36})-\frac{49}{6} + m<0\\\\\frac{49}{12} - \frac{49}{6} + m < 0\\\\\frac{49-98}{12} + m < 0\\\\\frac{-49}{12} + m < 0\\\\m < \frac{49}{12}[/tex]
The graph of [tex]y = 3x^2+7x+m[/tex] has two x-intercepts when m < 49/12
Learn more here: https://brainly.com/question/16502199
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
If you want to learn more, you can read:
https://brainly.com/question/23033812
