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

Answer:

For all $\frac{49}{12}>m$, the graph of given equation have two x-intercepts if the discriminant is positive.

Step-by-step 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.

$\frac{49}{12}>m$

For all $\frac{49}{12}>m$, the graph of given equation have two x-intercepts if the discriminant is positive.