State True or False.

The given equation $(x − 3) (2 x + 1) = x (x + 5)$ is a quadratic equation.

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True

False

answer is A.

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Detailed Solution

The given equation is

(x − 3) (2 x + 1) = x (x + 5)

.
We know that the standard form of a quadratic equation is

a x 2 + b x + c = 0, a ≠ 0

.
Expanding the given equation

(x − 3) (2 x + 1) = x (x + 5)

.
We get,

⇒ 2 x 2 + x − 6 x − 3 = x 2 + 5 x ⇒ 2 x 2 − 5 x − 3 = x 2 + 5 x ⇒ 2 x 2 − 5 x − 3 − x 2 − 5 x = 0 ⇒ x 2 − 10 x − 3 = 0

Compare the above equation with standard form of quadratic equation

a x 2 + b x + c = 0.

We get,
a = 1, b = -10, c = -3
Since, a ≠ 0 and a, b, c are real numbers, the given equation is a quadratic equation.
Therefore, the statement is true.
Hence, the correct option is 1.

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