Question

Aflati valorile parametrului real m,astfel incit ecuatia sa aiba o unicca solutie:
a)x² -mx+9=0
b)x²+3mx+m=0
c)2x²-2x+m=0
d)9x²-2x+m=6--mx

Answer 1

a)x²-mx+9=0
m²-36=0
(m-6)(m+6)=0
m=6  x²-6x+9=0 (x-3)²=0 x=3
m=-6 x²+6x+9=0 (x+3)²=0  x=-3

b)x²+3mx+m=0
9m²-4m=0
m(9m-4)=0
m=0
m=4/9

c)2x²-2x+m=0
4-8m=0
m=1/2

d)9x²-2x+m=6-mx
9x²-x(2-m)+m-6=0
(2-m)²-4·9(m-6)=0