Question # 15
Ifa

# 15
Ifa

Solution ( (a-b)^{2} x^{2}+2(a+b-2 c) x+1=0 )
disciménant
[
begin{aligned}
D &=frac{b^{2}-4 a c}{4(a+b-2 c)^{2}-4(a-b)^{2}}
&=4(a+b-2 c+a-b)(a+b-2 c-a+b)
&=4(2 a-2 c)(2 b-2 c)
&=16(a-c)(b-c)
end{aligned}
]
( because quad a0 )
( Rightarrow(a-c)(b-c)<0 )
( Rightarrow D<0 )
imaginary roots.

Solution