Question

The fifth question

${\text{5. One root of the equation 2x}}^2\text{-8x -m = 0 is}\frac{5}{2}\text{. Find the other root and the value of m.}$

Answer 1

Dear student
$$\begin{gathered} \mathrm{Since}\frac{5}{2}\mathrm{is}\mathrm{the}\mathrm{root}\mathrm{of}\mathrm{the}\mathrm{equation}2{\mathrm{x}}^2-8\mathrm{x}-\mathrm{m}=0 \\ \mathrm{So},\mathrm{it}\mathrm{will}\mathrm{satisfy}\mathrm{the}\mathrm{above}\mathrm{equation},\mathrm{we}\mathrm{get} \\ 2{\left(\frac{5}{2}\right)}^2-8\left(\frac{5}{2}\right)-\mathrm{m}=0 \\ \Rightarrow \frac{25}{2}-20-\mathrm{m}=0 \\ \Rightarrow \mathrm{m}=\frac{25}{2}-20 \\ \Rightarrow \mathrm{m}=\frac{-15}{2} \\ \mathrm{So},\mathrm{out}\mathrm{equation}\mathrm{is}2{\mathrm{x}}^2-8\mathrm{x}+\frac{15}{2}=0 \\ \mathrm{or}4{\mathrm{x}}^2-16\mathrm{x}+15=0 \\ \Rightarrow \mathrm{x}=\frac{16\pm \sqrt{256-240}}{8} \\ \Rightarrow \mathrm{x}=\frac{16\pm 4}{8} \\ \Rightarrow \mathrm{x}=\frac{5}{2}\mathrm{or}\mathrm{x}=\frac{3}{2} \end{gathered}$$
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