- For
f(x)=0to have 2 distinct real solutions it must beD>0where D stands for discriminant- Since D>0 it has to be (a^2)>4b in the first equation {solve from here}
- For
f(to have no real solutions it must bex^2-2x + c)=0D<0{solve from here}

Hint: For all quadratics, f(x) is greater or equal to 0.