Question:
Which of the following is a quadratic equation?
(a) $x^{2}-3 \sqrt{x}+2=0$
(b) $x+\frac{1}{x}=x^{2}$
(c) $x^{2}+\frac{1}{x^{2}}=5$
(d) $2 x^{2}-5 x=(x-1)^{2}$
Solution:
(d) $2 x^{2}-5 x=(x-1)^{2}$
A quadratic equation is the equation with degree 2 .
$\because 2 x^{2}-5 x=(x-1)^{2}$
$\Rightarrow 2 x^{2}-5 x=x^{2}-2 x+1$
$\Rightarrow 2 x^{2}-5 x-x^{2}+2 x-1=0$
$\Rightarrow x^{2}-3 x-1=0$, which is a quadratic equation
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