The sum of the roots of the equation x2 + px + q = 0 is

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The sum of the roots of the equation x² + px + q = 0 is equal to the sum of their squares, then

1. p² - q² = 0
2. p² + q² = 2q
3. p² + p = 2q
4. q² + q² = 2p
5. None of the above

Correct Option: C

Let α and β be the roots of the equation
x² + px + q = 0
Then, α + β = -p, α β = q
According to the question,
α + β = α² + β²
⇒ α + β = (α + β)² - 2α β
⇒ -p = p² - 2q ⇒ p² + p = 2q