Question

Which of the following is a quadratic equation?

• A. \( x^2 - 3\sqrt{x} + 2 = 0 \)
• B. \( x + \frac{1}{x} = x^2 \)
• C. \( x^2 + \frac{1}{x^2} = 5 \)
• D. \( 2x^2 - 5x = (x - 1)^2 \)

Hint:

A quadratic equation must have the highest exponent of \( x \) as 2.

Answer 1

The Correct Option is D

A quadratic equation is in the form:
\[ ax^2 + bx + c = 0, \quad \text{where } a \neq 0. \] Expanding (D):
\[ 2x^2 - 5x = x^2 - 2x + 1 \] \[ 2x^2 - 5x - x^2 + 2x - 1 = 0 \] \[ x^2 - 3x - 1 = 0 \] which is a quadratic equation.