Consider the following equations. I. x3 + 3(x2 + 2) + x = 0 II. x2 + 2(x + 1) + 2x2 = 0 III. 2x + 3 = 0 IV. (x + 3)2 + 2x = 0 Which two given equations are quadratic in nature?

An equation is called a quadratic equation if the highest power of the variable in it is 2. II. x2 + 2(x + 1) + 2x2 = 0 ⇒ x2 + 2x + 2 + 2x2 = 0 ⇒ 3x2 + 2x + 2 = 0 Since the highest power of the variable x is 2, this equation is quadratic in nature. IV. (x + 3)2 + 2x = 0 ⇒ x2 + 6x + 9 + 2x = 0 ⇒ x2 + 8x + 9 = 0 Since the highest power of the variable x is 2, this equation is quadratic in nature. Thus, among the given equations, the equations marked as II and IV are quadratic in nature. Hence, the correct answer is 4).

Consider the following equations. I. x3 + 3(x2 + 2) + x = 0 II. x2 + 2(x + 1) + 2x2 = 0 III. 2x + 3 = 0 IV. (x + 3)2 + 2x = 0 Which two given equations are quadratic in nature?

An equation is called a quadratic equation if the highest power of the variable in it is 2. II. x2 + 2(x + 1) + 2x2 = 0 ⇒ x2 + 2x + 2 + 2x2 = 0 ⇒ 3x2 + 2x + 2 = 0 Since the highest power of the variable x is 2, this equation is quadratic in nature. IV. (x + 3)2 + 2x = 0 ⇒ x2 + 6x + 9 + 2x = 0 ⇒ x2 + 8x + 9 = 0 Since the highest power of the variable x is 2, this equation is quadratic in nature. Thus, among the given equations, the equations marked as II and IV are quadratic in nature. Hence, the correct answer is 4).