Mathematics - Quadratic Equation Question with Solution | TestHub

$x^n+ax+b=\left(x-{\alpha }_1\right)\left(x-{\alpha }_2\right)\dots .\left(x-{\alpha }_n\right)$

differentiate both sides with respect to $x$.

$$\begin{array}{rl}n{x}^{n-1}+a& =\left(x-{\alpha }_2\right)\dots \left(x-{\alpha }_n\right)+\left(x-{\alpha }_1\right)\left(\frac{d}{dx}\left(x-{\alpha }_2\right)\dots \left(x-{\alpha }_n\right)\right)\\ \text{ put }x& ={\alpha }_1\\ n{\alpha }_1^{n-1}+a& =\left({\alpha }_1-{\alpha }_2\right)\left({\alpha }_1-{\alpha }_3\right)\dots \left({\alpha }_1-{\alpha }_n\right)\end{array}$$