Question

Find the roots of the equation $f\left(x\right)=(b-c)x^2+(c-a)x+(a-b)=0$.

Answer 1

Clearly x=1 is a root of the equationbecause f(1)=0 If the other root is $\alpha$ then product of the roots
$\alpha 1=\frac{a-b}{b-c}$
Thus the roots are $\frac{a-b}{b-c}$ and 1