Question

Which of the following is not a quadratic equation?

Options

• 3x – x² = x² + 5

• (x + 2)² = 2(x² – 5)

• `(sqrt(2)x + 3)^2 = 2x^2 + 6`

• (x – 1)² = 3x² + x – 2

Answer 1

`bb((sqrt(2)x + 3)^2 = 2x^2 + 6)`

Explanation:

(a) 3x – x² = x² + 5 

⇒ –2x² + 3x – 5 = 0   ...(Degree 2 → Quadratic)

(b) (x + 2)² = 2(x² – 5)

⇒ x² + 4x + 4 = 2x² – 10

⇒ –x² + 4x + 14 = 0 (Degree 2 → Quadratic)

(c) `(sqrt(2)x + 3)^2 = 2x^2 + 6` 

⇒ LHS = `2x^2 + 6sqrt(2)x + 9`, 

Subtract RHS gives `6sqrt(2)x + 3 = 0` (Degree 1 → Linear), so not quadratic.

(d) (x – 1)² = 3x² + x – 2

⇒ x² – 2x + 1 = 3x² + x – 2

⇒ –2x² – 3x + 3 = 0   ...(Degree 2 → Quadratic)

A quadratic must have highest power 2 (ax² + bx + c = 0 with a ≠ 0).