Finding the Sum of Roots (SoR) and Product of Roots (PoR)

2.6 Finding the Sum of Roots (SoR) and Product of Roots (PoR)

Example
Find the sums and products of the roots of the following equations.
a. $x^2+7x-<!--\; -\; -->3=0$
b. $x(x-<!--\; -\; -->1)=5(1-<!--\; -\; -->x)$

Answer:
(a)
$\begin{array}{l}{x}^2+7x-3=0\\ a=1,b=7,c=-3\\ \\ \text{Sum of Roots}\\ \alpha +\beta =-\frac{b}{a}=-\frac{7}{1}=-7\\ \text{Product of Roots}\\ \alpha \beta =\frac{c}{a}=\frac{-3}{1}=-3\end{array}$

(b)
$\begin{array}{l}x(x-1)=5(1-x)\\ x^2-x=5-5x\\ x^2-x+5x-5=0\\ x^2+4x-5=0\\ a=1,b=4,c=-5\\ \\ \text{Sum of Roots}\\ \alpha +\beta =-\frac{b}{a}=-\frac{4}{1}=-4\\ \\ \text{Product of Roots}\\ \alpha \beta =\frac{c}{a}=\frac{-5}{1}-5\end{array}$