Question

1. Check whether the following are quadratic equati(x-2)(x + 1) = (x - 1)(x+3)
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Answer 1

Given :

(x-2)(x + 1) = (x - 1)(x+3)

To find :

The equation is quadratic or not.

Solution :

$(x - 2)(x + 1) = (x - 1)(x + 3) \\ \\ = > {x}^{2} + x - 2x - 2 = {x}^{2} + 3x - x - 3 \\ \\ = > - x - 2 = + 2x - 3 \\ \\ = > 2x + x = - 2 + 3 \\ \\ = > 3x = 1 \\ \\ = > ( 3x - 1) = 0$

We know, the quadratic equation contains as,

$ax ^{2} + bx + c = 0$

where a not equal to 0

Therefore the given equation is not a quadratic equation.

Thanks :)

Answer 2

given :

$(x – 2) (x + 1) = (x – 1) (x + 3)$

We have:

$\: (x – 2) (x + 1) = (x – 1) (x + 3)$

$\: ⇒ x2 – x – 2 = x2 + 2x – 3$

$\: ⇒ x2 – x – 2 – x2 – 2x + 3 = 0$

$\: ⇒ –3x + 1 = 0$

Since –3x + 1 is a linear polynomial

∴ (x – 2) (x + 1) = (x – 1) (x + 3) is not quadratic equation.