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Check whether the following are quadratic equations:
$(2x – 1) (x – 3) = (x + 5) (x – 1)$
Given:
Given equation is $(2x – 1) (x – 3) = (x + 5) (x – 1)$
To do:
We have to check whether the given equation is quadratic.
Solution:
The standard form of a quadratic equation is $ax^2+bx+c=0$.
$(2x – 1) (x – 3) = (x + 5) (x – 1)$
$2x(x-3)-1(x-3)=x(x-1)+5(x-1)$
$2x^2-6x-x+3=x^2-x+5x-5$
$2x^2-x^2-7x-4x+3+5=0$
$x^2-11x+8=0$ is of the form $ax^2+bx+c=0$
Therefore, $(2x – 1) (x – 3) = (x + 5) (x – 1)$ is a quadratic equation.  
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