Question

For what values of m does the graph of y=3x^2+7x+m have two x-intercepts

Answer 1

to have 2 intercepts the discriminant must be > 0

7^2 - 4*3*m > 0
12m < 49
m < 4 1/12 answer

Answer 2

For all
`(49)/(12)>m`, the graph of given equation have two x-intercepts if the discriminant is positive.

Explanation:

A quadratic equation
`y=ax^2+bx+c` has

1. No x-intercept if
`(b^2-4ac)<0`.

2.One x-intercept if
`(b^2-4ac)=0`.

3. Two x-intercept if
`(b^2-4ac)>0`.

The given equation is

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

It is a quadratic equation. Here, a=3, b=7 and x=m. The graph of given equation have two x-intercepts if the discriminant is positive.

`(b^2-4ac)>0`

Put a=3, b=7 and x=m in the above inequality.

`7^2-4(3)(m)>0`

`49-12m>0`

Add 12m on both the sides.

`49>12m`

Divide both sides by 12.

`(49)/(12)>m`

For all
`(49)/(12)>m`, the graph of given equation have two x-intercepts if the discriminant is positive.