For 3x^2+4x+4=0
Discriminant= = -32
The solutions are
(-b+βx)/2a= (-2+2β-2)/3
(-b-βx)/2a= (-2-2β-2)/3
For 3x^2+2x+4=0
Discriminant= -44
The solutions
(-b+βx)/2a= (-1+β-11)/3
(-b-βx)/2a= (-1-β-11)/3
For 9x^2-6x+2=0
Discriminant= -36
The solutions
(-b+βx)/2a= (1+β-1)/3
(-b-βx)/2a= (1-β-1)/3
Step-by-step explanation:
Formula for the discriminant = bΒ²-4ac
let the discriminant be = x for the equations
The solution of the equations
= (-b+βx)/2a and = (-b-βx)/2a
For 3x^2+4x+4=0
Discriminant= 4Β²-4(3)(4)
Discriminant= 16-48
Discriminant= = -32
The solutions
(-b+βx)/2a =( -4+β-32)/6
(-b+βx)/2a= (-4 +4β-2)/6
(-b+βx)/2a= (-2+2β-2)/3
(-b-βx)/2a =( -4-β-32)/6
(-b-βx)/2a= (-4 -4β-2)/6
(-b-βx)/2a= (-2-2β-2)/3
For 3x^2+2x+4=0
Discriminant= 2Β²-4(3)(4)
Discriminant= 4-48
Discriminant= -44
The solutions
(-b+βx)/2a =( -2+β-44)/6
(-b+βx)/2a= (-2 +2β-11)/6
(-b+βx)/2a= (-1+β-11)/3
(-b-βx)/2a =( -2-β-44)/6
(-b-βx)/2a= (-2 -2β-11)/6
(-b-βx)/2a= (-1-β-11)/3
For 9x^2-6x+2=0
Discriminant= (-6)Β²-4(9)(2)
Discriminant= 36 -72
Discriminant= -36
The solutions
(-b+βx)/2a =( 6+β-36)/18
(-b+βx)/2a= (6 +6β-1)/18
(-b+βx)/2a= (1+β-1)/3
(-b-βx)/2a =( 6-β-36)/18
(-b-βx)/2a= (6 -6β-1)/18
(-b-βx)/2a= (1-β-1)/3