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 = 2x2 – 7x – 9
0 = x2 – 4x + 4
0 = 4x2 – 3x – 1
0 = x2 – 2x – 8
0 = 3x2 + 5x + 3

That is when b^2-4ac>0, that is when you have 2 real solutions

alright, so ax^2+bx+c=0

first one:
a=2, b=-7, c=-9
b^2-4ac=(-7)^2-4(2)(-9)=49+72>0, so this has 2 real solutions

2nd one
a=1, b=-4, c=4
b^2-4ac=(-4)^2-4(1)(4)=16-16=0, so this has only 1 real number solution

3rd
a=4, b=-3, c=-1
b^2-4ac=(-3)^2-4(4)(-1)=9+16>0, so this has 2 real number solutions

4th
a=1, b=-2, c=-8
b^2-4ac=(-2)^2-4(1)(-8)=4+32>0, so this has 2 real number solutions

5th
a=3, b=5, c=3
b^2-4ac=(5)^2-4(3)(3)=25-36<0, this has no real soltuions

answer is 1st, 3rd, 4th
those are
0 = 2x2 – 7x – 9
0 = 4x2 – 3x – 1
0 = x2 – 2x – 8