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L.H.S. = (2x – 1) (x – 3) = 2x 2 – 6x– + 3 = 2x 2 – 7x + 3 R.H.S. = (x + 5) (a – 1) = x 2 + 5x – x – 5 = x 2 + 4x – 5 ∴2x 2 – 7x + 3 = x 2 + 4x – 5 ⇒ 2x 2 –x 2 -7x–4x+ 3 + 5 = 0 ⇒ x 2 – 11x + 8 = 0 ∵ It is of the form ax 2 + bx + c = 0 where a = 1, b = –11, c = 8. Hence, the given equation is a quadratic equation.

Check whether the following are quadratic equations:
(2x –1) (x–3) = (x + 5)(x–1)

L.H.S. = (2x – 1) (x – 3)
= 2x² – 6x– + 3
= 2x² – 7x + 3
R.H.S. = (x + 5) (a – 1)
= x² + 5x – x – 5
= x² + 4x – 5
∴2x² – 7x + 3 = x² + 4x – 5
⇒ 2x² –x²-7x–4x+ 3 + 5 = 0
⇒ x² – 11x + 8 = 0
∵ It is of the form ax² + bx + c = 0 where a = 1, b = –11, c = 8.
Hence, the given equation is a quadratic equation.

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Quadratic Equations

Check whether the following are quadratic equations:(2x –1) (x–3) = (x + 5)(x–1)

Check whether the following are quadratic equations:
(2x –1) (x–3) = (x + 5)(x–1)