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State if the given statement is true or false, “ $(x - 2) (x + 1) = (x - 1) (x + 3)$ is a quadratic equation.”

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True

False

answer is B.

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Detailed Solution

It is given that

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

.
Simplifying the given equation,

⇒ x (x + 1) − 2 (x + 1) = x (x + 3) − 1 (x + 3) ⇒ x 2 + x − 2 x − 2 = x 2 + 3 x − x − 3 ⇒ 2 x − 2 x − 2 − 3 x + 3 = 0 ⇒ − 3 x + 1 = 0 ⇒ − 3 x = − 1

Hence,

x = \frac{1}{3}

.
A quadratic equation is of the form

a x^{2} + bx + c = 0

and the degree of the equation must be 2.
Thus, the above equation is not a quadratic equation rather a linear equation.
Therefore, the given statement is false.
“

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

is a linear equation.”
Hence, the correct option is 2.

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