Which of the following options represents a quadratic equation?
-
(x - 1)2 = 3x + 2
-
x3 - 7x2 + 2x2 = -5x2 + x3 + 5 + x
-
x (3x + 2) = 3x2 + 4x - 2
-
7x (2x2 + 3) = 3x + 5
Reveal answer
Fill a bubble to check yourself
A
Correct answer
Explanation
A quadratic equation is of the form ax^2 + bx + c = 0. Option A: (x-1)^2 = 3x+2 becomes x^2 - 2x + 1 = 3x + 2, which is x^2 - 5x - 1 = 0. This is quadratic.
AI explanation
A quadratic equation must have a highest degree of exactly 2. Expanding option A gives x2 - 2x + 1 = 3x + 2, which simplifies to x2 - 5x - 1 = 0, maintaining a degree of 2. The other options simplify to linear equations or higher degree cubic equations. Therefore, only the first expression remains a valid quadratic equation.