Răspuns:
Explicație pas cu pas:
f(x)=(a+1)x²+(2a+3)x+a+1 a≠-1
a)a=1 ⇒f(x)=2x²+5x+2 f(x)=0
x1,2=-5±√25-16/4=-5±3/4 x1=-2 x2=-1/2
b) a=11 f(x)=12x²+25x+12
x1,2=-25±√625-576/24=-25±7/24 x1=-32/24=-4/3 x2=-18/24=-3/4
x∈(-∞,-4/3)∪(-3/4,∞)
c)x1+x2+3x1x2=0
x1+x2=-(2a+3)/(a+1) x1x2=(a+1)/(a+1)=1
-(2a+3)/(a+1) +3=0 2a+3=3(a+1) 2a+3=3a+3 a=0
