Multiple choice

The question is based on the following pattern. The problems below contain a question and two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question. Find integers q, if the equation y2 - 2y + q = 0 has rational roots. (A) Only one of the roots is a natural number. (B) The product of the roots is zero.

  1. if the question can be answered by one of the statements alone, but cannot be answered by using the other statement alone.

  2. if the question can be answered by using either statement alone.

  3. if the question can be answered by using both the statement together, but cannot be answered by using either statement alone.

  4. if both the statements taken together are not sufficient and more information is required to solve the question.
Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

In the quadratic equation y2 - 2y + q = 0, the sum of the roots is 2. If statement A is true and one root is a natural number, the other root must also be a natural number to ensure their sum is the integer 2, which fixes both roots and uniquely determines q. If statement B is true and the product of the roots is zero, then q is zero, meaning the roots are 0 and 2. Either statement uniquely fixes the value of q. The result is that the question can be answered by using either statement alone.

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