Statement(A) : The difference of the roots of  $a{x}^2+bx+c=0$ is  $\frac{\sqrt{b^2-4ac}}{4a}$.

Statement(B) : If one root of  $a{x}^2+bx+c=0$ is n^th power of the other, then  ${\left(a{c}^n\right)}^{\frac{1}{n+1}}+{\left(a^{n}c\right)}^{\frac{1}{n+1}}+b=0$.