Odpowiedź:
a) 25x²-1=0
a= 25 b=0 c= -1
Δ= b²-4ac
Δ= 0²-4*25*(-1)
Δ= 0+100
Δ=100
√Δ= √100=10
x₁= -b+√Δ/2a
x₁= -0-10/2*25= -10/50= -1/5
x₂= -b+√Δ/2a
x₂= -0+10/2*25= 10/50= 1/5
x₁= -1/5 , x₂= 1/5
b) 4x²-5x=0
a= 4 b= -5 c= 0
Δ=b²- 4ac
Δ= (-5)² - 4*4*0
Δ= 25-0
Δ= 25
√Δ=√25=5
x₁= -b-√Δ/2a
x₁= 5-5/2*4= 0/8= 0
x₂= -b+√Δ/2a
x₂= 5+5/2*4= 10/8= 5/4
x₁= 0 x₂= 5/4
c) x(x+2)= -1
x²+2x= -1
x²+2x+1=0
(x+1)²=0
x+1=0
x= -1
d) x²-4x-5=0
a= 1 b= -4 c= -5
Δ=b²-4ac
Δ= (-4)²-4*1*(-5)
Δ= 16+20
Δ=36
√Δ=√36=6
x₁= -b-√Δ/2a
x₁= 4-6/2*1= -2/2= -1
x₂= -b+√Δ/2a
x₂= 4+6/2*1= 10/2 =5
x₁= -1 x₂=5
e) x(x+5)=4x(x-5)
x²+5x= 4x²-20x
x²+5x-4x²+20x=0
-3x²+25x=0
-x(3x-25)=0 /:(-1)
x(3x-25)=0
x₁=0 3x-25= 0
3x= 25/:3
x₂= 25/3
x₁=0 x₂= 25/3
