Question

If alpha and beta are the roots of the quadratic equations 9x²-24x+8=0,then find alpha + beta and alphabeta?

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{given}\mathrm{quadratic}\mathrm{equation}\mathrm{is}: \\ 9{\mathrm{x}}^2-24\mathrm{x}+8=0 \\ \mathrm{Comparing}\mathrm{it}\mathrm{with}\mathrm{standard}\mathrm{equation},{\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0,\mathrm{we}\mathrm{get} \\ \mathrm{a}=9;\mathrm{b}=-24;\mathrm{c}=8 \\ \mathrm{Now},\mathrm{\alpha }\mathrm{and}\mathrm{\beta }\mathrm{are}\mathrm{the}\mathrm{roots}\mathrm{of}\mathrm{the}\mathrm{above}\mathrm{equation}. \\ \mathrm{So},\mathrm{\alpha }+\mathrm{\beta }=-\frac{\mathrm{coefficient}\mathrm{of}\mathrm{x}}{\mathrm{coefficient}\mathrm{of}{\mathrm{x}}^2}=\frac{24}{9}=\frac{8}{3} \\ \mathrm{\alpha \beta }=\frac{\mathrm{constant}\mathrm{term}}{\mathrm{coefficient}\mathrm{of}{\mathrm{x}}^2}=\frac{8}{9} \end{gathered}$$