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


Asked by wiki @ in Mathematics viewed by 382 People

Answered by wiki @


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

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