The sum of the roots of the equation x 2 + px + q = 0 is equal to the sum of their squares, then

Q: The sum of the roots of the equation x 2 + px + q = 0 is equal to the sum of their squares, then

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

p2 - q2 = 0
p2 + q2 = 2q
p2 + p = 2q
q2 + q2 = 2p

Correct Answer: p2 + p = 2q

Explanation:

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

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