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Rainbow [258]
3 years ago
6

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

Mathematics
2 answers:
Irina18 [472]3 years ago
8 0

we are given

y=3x^2+7x+m

To find x-intercept means we have to find zeros

and for finding zeros , we will use quadratic formula

and we have it has two x-intercepts

so, it's discriminant must be greater than 0

so, we will find discriminant

D=\sqrt{b^2-4ac}

now, we can compare with

y=ax^2+bx+c

y=3x^2+7x+m

and then we can find a , b and c

a=3,b=7,c=m

now, we can find D

D=\sqrt{7^2-4*3*m}

D=\sqrt{49-12m}

It has two x-intercepts

so,

D=\sqrt{49-12m}>0

now, we can solve for m

49-12m>0

12m

m............Answer

raketka [301]3 years ago
7 0

Answer:

m < \frac{49}{12}

Step-by-step explanation:

y= 3x^2+7x+m

a = 3

b=7

c = m

The graph is a parabola .

The Parabola with minimum point x=\frac{-b}{2a}  

                                                         x=\frac{-7}{2\times 3}  

                                                          x=\frac{-7}{6}                                                            

Now, To have 2 x intercepts, the value at the minimum point must be less than 0 i.e. 3x^2+7x+m

So, Substitute the minimum value in the equation

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}

Thus  the graph of y= 3x^2+7x+m have two x-intercepts when m < \frac{49}{12}

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