Question

If the arithmetic mean of the roots of the equation x² – 6x + 8 = 0 is ________.

Answer 1

Let the roots of the quadratic equation x² – 6x + 8 = 0 be $\alpha \mathrm{and}\beta$.

$$\begin{gathered} \mathrm{Sum}\mathrm{of}\mathrm{the}\mathrm{roots}=-\frac{-6}{1} \\ \Rightarrow \alpha +\beta =6 \\ \mathrm{Arithmetic}\mathrm{Mean}\mathrm{of}\mathrm{the}\mathrm{roots}=\frac{\alpha +\beta }{2} \\ =\frac{6}{2} \\ =3 \end{gathered}$$

Hence, the arithmetic mean of the roots of the equation x² – 6x + 8 = 0 is 3.