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Written By
Kashifa Jafar
Reviewed By
Sameena Begum
Published
February 27, 2025
Last Updated
October 14, 2026
This article is part of
Education
For What Values Of M Does Graph Of Y = 3×2+7x+M Have 2X-Intercepts?
In this article, we explain the solution of “For What Values Of M Does The Graph Of Y = 3×2 + 7x + M Have Two X-Intercepts?”. First of all, we will talk about top websites which give so much information about every solution.
We have so many good websites that have so much knowledge about problems. So, let’s have a look!
quora.com
For the x-intercept, put y=0.
the equation becomes, 3×2 +7x +m =0
Now find the discriminant, D=(49 – 4*3*m) >0 (For the roots should be distinct and accurate)
49>12m
or, m<49/12
Thus the value of m lies between (-infinity, 49/12 ).
protonstalk.com
The graph is a parabola with the most petite point. So, Substitute the smallest value in the equation y = 3x^2 + 7x + m. Thus the graph has two x-intercepts. The value at a minor point must be less than 0. The chart is a parabola with the smallest where x= -b/2a = -7/6.i.e
3(49/36) – 49/6 + m < 0
49/12 – 49/6 + m < 0
(49-98)/12 + m < 0
-49/12 + m < 0
m < 49/12
wyzant.com
The graph is a parabola with the smallest where x= -b/2a = -7/6. You should sketch it!
To have two x-intercepts, the value at a minor point must be less than 0, i.e.
3(49/36) – 49/6 + m < 0
49/12 – 49/6 + m < 0
(49-98)/12 + m < 0
-49/12 + m < 0
m < 49/12
cuemath.com
Question: For What Values Of M Does The Graph Of Y = 3×2 + 7x + M Have Two X-Intercepts?
Solution: The above equation is a polynomial that, when plotted, looks like a parabola. It is understood that the value of the variable “y” at the point of intersection with the x-axis is “zero” when the parabola crosses the x-axis. As a result, by changing the value of “y” in the following equation to zero, we get:
0 = 3×2 + 7x + m
To factorise the preceding quadratic equation, we must first determine the value of m. The remaining two components of the equation, 3×2 and 7x, may be used to calculate the probable value of “m.” As a result, the proper value of m is “2.” We may factorise the following equation by substituting the value of m.
0 = 3×2 + 7x + 2
0 = (x + 2)(3x + 1)
As no other value of m can factorise the above equation, m = 2 is a unique number. When the equation above is solved, we get two discounts of x when y = 0, x = -2 and x = -1/3. Hence, the equation will have two intercept values for m = 2.
What m values cause the graph of y = 3×2 + 7x + m to have two x-intercepts?
Summary:
The parabola contacts the x-axis twice at (-2, 0) and (-1/3, 0) for m = 2.
gauthmath.com – graph
Question
Answer
C
Explanation:
A
Depending on the number of possible solutions:
Rearrange the unknown terms to the left side of the equation as follows:
Lower the most common element that exists on both sides of the inequality:
Divide both sides of the inequality by the variable’s coefficient:
Rewrite this as a fraction:
Get the outcome:
False
True or false?
Written By
Kashifa Jafar
Business & Digital Trends Writer ·
4+ Years Experience
Kashifa Jafar is a business and digital trends writer at Businessian with 4+ years of experience in content writing and digital publishing. She covers business, entrepreneurship, marketing, e-commerce, digital trends and practical topics that help readers better understand the changing business landscape.
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Reviewed By
Sameena Begum
Business & Digital Content Reviewer ·
8 Years Experience
Sameena Begum is a business and digital content reviewer at Businessian. She reviews selected content for clarity, organisation, consistency, readability and overall editorial quality.
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