Which of the following represents a quadratic equation?

Correct option is D

Given:

Given quadratic equation are :

​$$(x - 7)(x + 2) = (x - 2)(x)$$​​

​$$(x + 3)(x - 4) =x^2 + 2x + 12$$​​

​$$(3x + 4)x = 3x^2 + 16$$​​

​$$(x + 2)(x + 2)(x - 1) = x^3 + 5x^2 + 6x + 4$$​​

Formula Used:

For a equation to be a quadratic equation the degree of equation should be 2 and power of x cannot be in root or negative

Standard quadratic equation is in the form of $$ax^2 +bx +c = 0$$​​

Solution:

Checking the given equation

​$$(x - 7)(x + 2) = (x - 2)(x)$$​​

​$$x^2 +2x-7x -14 = x^2 - 2x$$​​

3x-14

The degree is 1 hence, it is a not quadratic equation

​$$(x + 3)(x - 4) =x^2 + 2x + 12$$​​

​$$x^2 -4x +3x -12 = x^2 + 2x + 12$$​​

3x+24 = 0

The degree is 1 hence, it is a not quadratic equation

​$$(3x + 4)x = 3x^2 + 16$$​​

​$$3x^2 +4x = 3x^2 +16$$​​

4x=16

The degree is 1 hence, it is a not quadratic equation

​$$(x + 2)(x + 2)(x - 1) = x^3 + 5x^2 + 6x + 4$$​​

​$$(x^2 +4x +4)(x-1) = x^3 + 5x^2 + 6x + 4$$​​

​$$x^3 +4x^2 +4x -x^2 -4x -4 = x^3 + 5x^2 + 6x + 4$$​​

​$$2x^2 +6x +8 = 0$$​​

The degree is 2 and it is in standard form hence it is a quadratic equation