Question

Aflati valorile parametrului real m, astfel incit ecuatia sa aiba o unica solutie.
b. x²+3mx+m=0

c. 2x²-2x+m=0

d. 9x²-2x+m=6-mx

Answer 1

a)x²+3mx+m=0
Δ=b²-4ac
Δ=9m²-4m
9m²-4m=0
m(9m-4)=0
m1=0
9m-4=0
9m=4
m2=4/9
daca m=0 atunci avem x1=x2=0
daca m=4/9 avem x²+3·4/9x+4/9=0
x²+4x/3+4/9=0
9x²+12x+4=0
Δ=144-144=0
x1=x2=-12/18=-6/9=-2/3

b(x²-2x+m=0
Δ=4-4m
4-4m=0
-4m=-4    inmultim -1
m=4/4
m=1
x²-2x+1=0
Δ=4-4=0
x1=x2=2/2=1

c)9x²-2x+m=6-mx
9x²-2x+mx+m-6=0
9x²+(m-2)x+m-6=0
Δ=(m-2)²-36(m-6)=m²-4m+4-36m+216=m²-40m+220
m²-40m+220=0
Δ=1600-880=720
m1=(40-12√5)/2=2(20-6√5)/2=20-6√5
m2=20+6√5
e mai complicat