Question

Which of the following is a quadratic equation?

Options

• `x^2 - 2sqrt(x) + 7 = 0`

• 2x² – 5x = (x – 1)²

• `x - 1/x = 2x^2`

• `x^2 + 1/x^2 = 2`

Answer 1

2x² – 5x = (x – 1)²

Explanation:

A quadratic equation is a polynomial equation of degree 2 (form ax² + bx + c = 0, a ≠ 0).

1. `x^2 - 2sqrt(x) + 7 = 0` contains `sqrt(x)(x^(1/2))`, not a polynomial in x → not quadratic.
2. 2x² – 5x = (x – 1) ⇒ 2x² – 6x + 1 = 0, a polynomial of degree 2 ⇒ quadratic.
3. `x - 1/x = 2x^2` ⇒ multiplying by x gives 2x³ – x² + 1 = 0, degree 3 ⇒ not quadratic.
4. `x^2 + 1/x^2 = 2` ⇒ multiplying by x² gives x⁴ – 2x² + 1 = 0, degree 4 (quartic) ⇒ not quadratic (though it is quadratic in y = x²).