Check Whether The Following Are Quadratic Equations (2X−1)(X−3)=(X+5)(X−1)

Given equation: (2x − 1)(x − 3) = (x + 5)(x − 1)\)

=\( 2x (x – 3) – 1 (x – 3) = x (x – 1) + 5 (x – 1)\)

=\( 2x^{2} – 6x – x + 3 = x^{2} – x + 5x – 5\)

=\( 2x^{2} – 6x – x + 3 – x^{2} + x – 5x + 5 = 0\)

=\( 2x^{2} – x^{2} – 6x – x + x + 5x + 3 + 5 = 0 \)

=\( x^{2} – 11x + 8 = 0 \)

The obtained equation\( x^{2} – 11x + 8 = 0 is in the form of ax^{2} + bx + c = 0\)

where a = 1, b = -11 and c = 8

Therefore, the given equation (2x − 1)(x − 3) = (x + 5)(x − 1) is a quadratic equation

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