for the equation.
\(c x^{2}+a x+b=0\)
the quadratic coefficients are
\(a=c . b=a . c=b\)
if \(\alpha\) and \(\beta\) are the roots of equation then.
sum of roots \(=\frac{-b}{a} \alpha+\beta=\frac{-a}{c}\)
product of root \(\alpha \beta=\frac{c}{a}=\frac{b}{c}\)lternatively.
let \(x=\alpha . x=\beta\)
\((x-\alpha)(x-\beta)=0\)
\(x^{2}-(\alpha+\beta) x+\alpha \beta=0\)
Now. \(x^{2}+\frac{a}{c} x+\frac{b}{c}=0 \ldots \ldots \ldots\) (ii)
comparing (a) and (ii).
\(A \beta=\frac{b}{c}\)