Question

Choose the correct answer from the given four options :

Which of the following is a quadratic equation?

विकल्प

• (x – 2) (x + 1) = (x – 1) (x – 3)

• (x + 2)³ = 2x(x² – 1)

•  x² + 3x + 1 = (x – 2)²

• 8(x – 2)³ = (2x – 1)³ + 3

Answer 1

(x – 2) (x + 1) = (x – 1) (x – 3)
⇒ x² + x – 2x – 2 = x² – 3x – x + 3
⇒ 3x + x – 2x + x = 3 + 2
⇒ 3x = 5
It is not a quadratic equation

(x + 2)³ = 2x(x² - 1)
x³ + 6x² + 12x + 8 = 2x³ – 2x
x³ + 6x² + 12x + 8 – 2x³ + 2x = 0
–x³ + 6x² + 14x + 8 = 0
It is not a quadratic equation.

x² + 3x + 1 = (x – 2)²
x² + 3x + 1 = x² – 4x + 4
3x + 1 + 4x – 4 = 0
⇒ 7x – 3 = 0
It is not a quadratic equation.

8(x – 2)³ = (2x – 1)³ + 3
8(x³ – 6x² + 12x - 8) = 8x³ – 12x² + 6x – 1+ 3
8x³ – 48x² + 96x – 64 – 8x³ + 12x² – 6x + 1 – 3 = 0
–36x² + 90x – 66 = 0
It is a quadratic equation.