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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?

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II and III

I and II

III and IV

II and IV

answer is D.

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Detailed Solution

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).

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