a) x²-14x+33=(x-11)(x-3)
a=1
b=-14
c=33
Δ=(-14)² -4x33=196-132=64
x₁,₂=(14+/-√64)/2=(14+/-8)/2
x₁=(14+8)/2=11
x₂=(14-8)/2=3
verificare
x₁+x₂=-b/a 11+3=14/1 14=14
x₁ × x₂=c/a 11×3=33/1 33=33
b) x²+12x-28=(x+14)(x-2)
a=1
b=12
c=-28
Δ=(12)² -4x(-28)=144+112=256
x₁,₂=(-12+/-√256)/2=(-12+/-16)/2
x₁=(-12+16)/2=2
x₂=(-12-16)/2=-14
verificare
x₁+x₂=-b/a 2-14=-12/1 -12=-12
x₁ × x₂=c/a 2×(-14)=-28/1 -28=-28
e) x²+12x+35=(x+7)(x+5)
a=1
b=12
c=35
Δ=(12)² -4x35=144-140=4
x₁,₂=(12+/-√4)/2=(12+/-2)/2
x₁=(-12+2)/2=-5
x₂=(-12-2)/2=-7
verificare
x₁+x₂=-b/a -5-7=-12/1 -12=-12
x₁ × x₂=c/a (-5)×(-7)=35/1 35=35
c) x²-15x+56=(x-8)(x-7)
a=1
b=-15
c=56
Δ=(-15)² -4x56=225-224=1
x₁,₂=(15+/-√1)/2=(15+/-1)/2
x₁=(15+1)/2=8
x₂=(15-1)/2=7
verificare
x₁+x₂=-b/a 7+ 8=15/1 15=15
x₁ × x₂=c/a 8× 7=56/1 56=56
f) 3x²+8x+5=(x+1)(x+5/3)
a=3
b=8
c=5
Δ=(8)² -4x5x3=64-60=4
x₁,₂=(-8+/-√4)/6=(-8+/-2)/6
x₁=(-8+2)/6=-1
x₂=(-8-2)/6=-5/3
verificare
x₁+x₂=-b/a -1-5/3=-8/3 -8/3=-8/3
x₁ × x₂=c/a (-1)×(-5/3)=5/3 5/3=5/3
h) x²+2√2x+1=(x+√2-1)(x+√2+1)
a=1
b=2√2
c=1
Δ=(2√2)² -4x1=8-4=4
x₁,₂=(-2√2+/-√4)/2=(-2√2+/-2)/2
x₁=(-2√2+2)/2=-√2+1
x₂=(-2√2-2)/2=-√2-1
verificare
x₁+x₂=-b/a -√2+1 -√2-1=-2√2/1 -2√2=-2√2
x₁ × x₂=c/a (-√2+1)×(-√2-1)=1 1=1
