Question

If -nx2 + tx + c = 0, what is x equal to?

Answer 1

`f(x)=-nx^2+tx+c=0\\\\ \Delta=t^2-4\cdot(-n)\cdot c=t^2+4cn\\\\ 1.\\ \Delta<0 \Rightarrow x\in\emptyset\\\\ 2.\\ \Delta=0\\ x=(-t)/(2\cdot(-n))=(t)/(2n)\\\\ 3.\\ \Delta>0\\ √(\Delta)=√(t^2+4cn)\\ x_1=(-t-√(t^2+4cn))/(2\cdot(-n))=(t+√(t^2+4cn))/(2n)\\ x_2=(-t+√(t^2+4cn))/(2\cdot(-n))=(t-√(t^2+4cn))/(2n)\\`