Question

check whether the following are quadratic equations (2x-1) (x-3)=(x+5) (x-1)​

Answer 1

(2x-1) (x-3)=(x+5) (x-1)​

2x^2 - x - 6x + 3 =  x^2 + 5x - x - 5

x^2 - 11x + 8 = 0

This is a quadratic equation

Hope I helped

Answer 2

${\huge{\purple{\mathbb{\bold{ANSWER}}}}}$

${\small{\blue{\bold{\underline{Standard\:Form\:of\:Quadratic\:Equation:-}}}}}$

$\implies \: ax {}^{2} + bx + c = 0$

${\large{\blue{\bold{\underline{Given:-}}}}}$

$\implies(2x - 1)(x - 3) = (x + 5)(x - 1) \\ \\ \implies \: 2x {}^{2} - 6x - x + 3 = {x}^{2} - x + 5x - 5 \\ \\ \implies2x {}^{2} - 7x + 3 = {x}^{2} + 4x - 5 \\ \\ \implies2 {x}^{2} - {x}^{2} - 7x - 4x + 3 + 5 = 0 \\ \\ \implies \: {x}^{2} - 11x + 8 = 0$

Clearly it satisfies the standard form of a quadratic equation where ,

▪︎ a = 1.

▪︎ b = (-11).

▪︎ c = 8.

☆ Hence it is a quadratic equation.

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