Question

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

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,

$\begin{array}{rcl}{(\mathrm{x}+1)}^2& =& 2(\mathrm{x}-3)\\ {\mathrm{x}}^2+1+2\mathrm{x}& =& 2\mathrm{x}-6\left[\mathrm{Note}:{(\mathrm{a}+\mathrm{b})}^2={\mathrm{a}}^2+{\mathrm{b}}^2+2\mathrm{ab}\right]\\ {\mathrm{x}}^2+2\mathrm{x}-2\mathrm{x}+1+6& =& 0\\ {\mathrm{x}}^2+7& =& 0\\ {\mathrm{x}}^2+0\mathrm{x}+7& =& 0\\ & & \end{array}$

$\because$The above equation is in the form of ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$, where $\mathrm{a}=1,\mathrm{b}=0$ and $\mathrm{c}=7$

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