Question

Va rog mult ajutati-ma la acest exercitiu:
Utilizind relatiile lui Viete,rezolvati in R ecuatia:
a)x^2-5x+6=0,
b)x^2+5x-14=0.

Answer 1

delta=b^2-4ac=5^2-4*1*6=25-24=1
x1=-b^2+radical din delta=5+1=6=3
                 2a                    2    2
x2=5-1=4=2
        2  2
S={2;3}

Answer 2

a)x²-5x+6=0
a=1
b=-5
c=6
S=x₁+x₂=-b/a=5/1=5
deci S=5
P=x₁x₂=c/a=6/1=6
deci P=6

sau Δ=b²-4ac
Δ=25-4·6=1
x₁=(5-1)/2=4/2=2
x₂=(5+1)/2=6/2=3
x∈{2,3}

b)x²+5x-14=0
a=1
b=5
c=-14
S=-b/a=-5/1=-5
P=c/a=-14/1=-14

Δ=25+56=81
x₁=(-5+9)/2=4/2=2
x₂=(-5-9)/2=-14/2=-7
x∈{-7,2}