Question

Check whether the following are quadratic equations ${\mathrm{x}}^2-2\mathrm{x}=(-2)(3-\mathrm{x})$

Answer 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,

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

$\because$The above equation is in the form of ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$, where $\mathrm{a}=1,\mathrm{b}=-4$ and $\mathrm{c}=6$

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