Question

1) -2XLA A DOUA+5X-2=0
2) x la a doua -2x+1=0
3) 4x la a doua -2x+3=0

Answer 1

1)

-2x²+5x-2=0

Δ=b²-4ac=25-4×(-2)×(-2)=25-16=9

Δ>0 are 2 solutii reale si distincte

x₁=(-b+√Δ/2a=(-5+3)/[2×(-2)]=2/-4=-1/2

x₂=(-5-3)/-4=2

Δ=0 are 2 solutii reale identice

2)

x²-2x+1=0

Δ=b²-4ac=4-4=0

x₁=x₂=(2)/(-4)= - 1/2

3)

4x²-2x+3=0

Δ=b²-4ac=4-4×(4)×(3)=4-48= - 44

x₁=(-b+√Δ/2a=(2+√44)/[2×(4)]=(2+2√11)/8=(1+√11)/4

x₂=(1-√11)/4

Δ<0  nu are solutii reale dar are solutii complexe