Question

Question number 5

5. Solve the following quadratic equation by using the quadratic formula :
x² + 6 = 8x

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{given}\mathrm{quadratic}\mathrm{equation}\mathrm{is}, \\ {\mathrm{x}}^2+6=8\mathrm{x} \\ \Rightarrow {\mathrm{x}}^2-8\mathrm{x}+6=0 \\ \mathrm{Comparing}\mathrm{the}\mathrm{above}\mathrm{equation}\mathrm{with}{\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0,\mathrm{we}\mathrm{get} \\ \mathrm{a}=1;\mathrm{b}=-8;\mathrm{c}=6 \\ \mathrm{Now},\mathrm{D}={\mathrm{b}}^2-4\mathrm{ac} \\ ={\left(-8\right)}^2-4\left(1\right)\left(6\right) \\ =64-24 \\ =40>0 \\ \mathrm{Now},\mathrm{the}\mathrm{roots}\mathrm{are}\mathrm{given}\mathrm{by} \\ \mathrm{x}=\frac{-\mathrm{b}+\sqrt{\mathrm{D}}}{2\mathrm{a}}\mathrm{and}\mathrm{x}=\frac{-\mathrm{b}-\sqrt{\mathrm{D}}}{2\mathrm{a}} \\ \Rightarrow \mathrm{x}=\frac{8+\sqrt{40}}{2\times 1}\mathrm{and}\mathrm{x}=\frac{8-\sqrt{40}}{2\times 1} \\ \Rightarrow \mathrm{x}=\frac{8+2\sqrt{10}}{2}\mathrm{and}\mathrm{x}=\frac{8-2\sqrt{10}}{2} \\ \Rightarrow \mathrm{x}=4+\sqrt{10}\mathrm{and}\mathrm{x}=4-\sqrt{10} \end{gathered}$$