Which of the following equations is quadratic ?
(1) $x^{2} + 2 x + 11 = 0$
(2) $x^{2} - 2 x + 5 = x^{2}$
(3) ${(x + 2)}^{2} = 2 x^{2}$

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Solution

General form of a quadratic equation is
$a x^{2} + b x + c = 0$
(1) $x^{2} + 2 x + 11 = 0$ is in the form of the general quadratic equation.
(2) $x^{2} - 2 x + 5 = x^{2}$
$\Rightarrow - 2 x + 5 = 0$
It is not in the form of quadratic equation.
(3) ${(x + 2)}^{2} = 2 x^{2}$
$\Rightarrow x^{2} + 4 + 4 x = 2 x^{2} \Rightarrow x^{2} - 4 x - 4 = 0$
It is also in the form of a quadratic equation.
Hence, (1) and (3) are quadratic equations.

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Which of the following equations is quadratic ? (1) x2+2x+11=0 (2) x2-2x+5=x2 (3) x+22=2x2

Which of the following equations is quadratic ?
(1) $x^{2} + 2 x + 11 = 0$
(2) $x^{2} - 2 x + 5 = x^{2}$
(3) ${(x + 2)}^{2} = 2 x^{2}$