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For which value of a does the sum of the squares of the roots of the quadratic equation x² - (a - 2)x - a - 1 = 0 become minimum?

1. 1
2. 0
3. 3
4. 2

Correct answer: 1

Solution

The sum of the squares of the roots of a quadratic equation can be expressed in terms of its coefficients. By analyzing the expression derived from the equation, we find that the minimum occurs when a equals 1, leading to the least value for the sum of the squares.

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