Answer: [tex]0=2x^2-7x-9\\0=4x^2-3x-1\\0=x^2-2x-8[/tex]
Step-by-step explanation:
We know that the standard quadratic equation is ax^2+bx+c=0
Let's compare all the given equation to it and , find discriminant.
1. a=2, b= -7, c=-9
[tex]b^2-4ac=(-7)^2-4(2)(-9)=49+72>0[/tex]
So it has 2 real number solutions.
2. a=1, b=-4, c=4
[tex]b^2-4ac=(-4)^2-4(1)(4)=16-16=0[/tex]
So it has only 1 real number solution.
3. a=4, b=-3, c=-1
[tex]b^2-4ac=(-3)^2-4(4)(-1)=9+16=25>0[/tex]
So it has 2 real number solutions.
4. a=1, b=-2, c=-8
[tex]b^2-4ac=(-2)^2-4(1)(-8)=4+32=36>0[/tex]
So it has 2 real number solutions.
5. a=3, b=5, c=3
[tex]b^2-4ac=(5)^2-4(3)(3)=25-36=-9<0[/tex]
Thus it does not has real solutions.
The quadratic equations that has real number solutions are 0 = 4x^2 – 3x – 1, 0 = x^2 – 2x – 8 and 2x^2 – 7x – 9
The formula for finding the discriminant is [tex]b^2-4ac[/tex]
For the quadratic equation [tex]2x^2 - 7x - 9 = 0[/tex]
[tex]b^2-4ac = (-7)^2-4(2)(-9) = 49 + 72 =121 [/tex]
This equation will have two real number solutions
For the quadratic equation [tex]4x^2 - 3x - 1 = 0[/tex]
[tex]b^2-4ac = (-3)^2-4(4)(-1) = 9 + 16 =25 >0[/tex]
This equation will have two real number solutions
For the quadratic equation [tex]x^2 - 2x - 8 = 0[/tex]
[tex]b^2-4ac = (-2)^2-4(1)(-8) = 4 + 32 =36>0 [/tex]
This equation will have two real number solutions
Learn more on discriminant here: https://brainly.com/question/1537997
