Check whether the following are quadratic equations: $(2\mathrm{x}-1)(\mathrm{x}-3)=(\mathrm{x}+5)(\mathrm{x}-1)$

Quadratic equation:

Quadratic equations are the polynomial equations of degree $2$ in one variable of type ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}$where $\mathrm{a},\mathrm{b},\mathrm{c},\in \mathrm{R}$ and$\mathrm{a}\ne 0$.

On expanding,

$\begin{array}{rcl}(2\mathrm{x}-1)(\mathrm{x}-3)& =& (\mathrm{x}+5)(\mathrm{x}-1)\\ 2{\mathrm{x}}^2-6\mathrm{x}-1\mathrm{x}+3& =& {\mathrm{x}}^2-1\mathrm{x}+5\mathrm{x}-5\\ 2{\mathrm{x}}^2-7\mathrm{x}+3& =& {\mathrm{x}}^2+4\mathrm{x}-5\\ 2{\mathrm{x}}^2-{\mathrm{x}}^2-7\mathrm{x}-4\mathrm{x}+3+5& =& 0\\ 1{\mathrm{x}}^2-11\mathrm{x}+8& =& 0\end{array}$

$\because$The above equation is in the form of ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$, where $\mathrm{a}=1,\mathrm{b}=-11$ and $\mathrm{c}=8$

Therefore, the given equation $(2\mathrm{x}-1)(\mathrm{x}-3)=(\mathrm{x}+5)(\mathrm{x}-1)$ is a quadratic equation.