The complete question is
"Substitute the values for a, b, and c into b2 – 4ac to determine the discriminant. Which quadratic equations will have two real number solutions? (The related quadratic function will have two x-intercepts.) Check all that apply.
0 = 2x^2 – 7x – 9
0 = 4x^ 2 – 3x – 1
The quadratic equations that have real number solutions are; 4x^2 – 3x – 1, and 2x^2 – 7x – 9.
<h3>What is the formula for Discriminant?</h3>
The formula for finding the discriminant is
![b^2 - 4ac](https://tex.z-dn.net/?f=b%5E2%20-%204ac)
The solution contains the term
which will be:
Real and distinct if the discriminant is positive
Real and equal if the discriminant is 0
Non-real and distinct roots if the discriminant is negative
For the quadratic equation ![2x^2 - 7x - 9](https://tex.z-dn.net/?f=2x%5E2%20-%207x%20-%209)
![= (-7) ^2 - 4( 2) ( -9)\\\\= 49 + 72 = 121](https://tex.z-dn.net/?f=%3D%20%28-7%29%20%5E2%20-%204%28%202%29%20%28%20-9%29%5C%5C%5C%5C%3D%2049%20%2B%2072%20%3D%20121)
This equation has two real number solutions.
For the quadratic equation ![4x^ 2 - 3x- 1](https://tex.z-dn.net/?f=4x%5E%202%20-%203x-%201)
![= (-3) ^2 - 4( 4) ( -1)\\\\= 9 + 16 = 25](https://tex.z-dn.net/?f=%3D%20%28-3%29%20%5E2%20-%204%28%204%29%20%28%20-1%29%5C%5C%5C%5C%3D%209%20%2B%2016%20%3D%2025)
This equation will have two real number solutions.
Learn more on discriminant here:
brainly.com/question/1537997
#SPJ1