Question

Which one is the quadratic equation?

From the following equations, which one is the quadratic equation?

Options

• `5/x - 3 = x^2`

• x(x + 5) = 2

• n – 1 = 2n

• `1/x^2(x + 2)` = x

Answer 1

x(x + 5) = 2

Explanation:

The general form of a quadratic equation is ax² + bx + c = 0.

i. `5/x - 3 = x^2`

`(5 - 3x)/x = x^2`

5 – 3x = x³

x³ + 3x – 5 = 0

⇒ This is not a quadratic equation.

ii. x(x + 5) = 2

x² + 5x = 2

x² + 5x − 2 = 0

⇒ This is a quadratic equation.

iii. n − 1 = 2n 

This is not a quadratic equation.

iv. `1/x^2 (x + 2)` = x

x + 2 = x³

x³ – (x + 2) = 0

x³ – x – 2 = 0

⇒ This is not a quadratic equation.