The roots and of a quadratic equation, satisfy the relations + = ^2+ ^2 and = ^2 ^2. What is the number of such quadratic equations?

NDA 2020 Mathematics question

The roots and of a quadratic equation, satisfy the relations and . What is the number of such quadratic equations?

Answer: (D)

Let , . or , and . If : or , giving $

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Question ID VK-029215