Let a, b $ \in $ R, a $ \ne $ 0 be such that the equation, ax2 – 2bx + 5 = 0 has a repeated root $\alpha $, which is also a root of the equation, x2 – 2bx – 10 = 0. If $\beta $ is the other root of this equation, then $\alpha $2 + $\beta $2 is equal to :

Question

Let a, b $ \in $ R, a $ \ne $ 0 be such that the equation, ax² – 2bx + 5 = 0 has a repeated root $\alpha $, which is also a root of the equation, x² – 2bx – 10 = 0. If $\beta $ is the other root of this equation, then $\alpha $² + $\beta $² is equal to :

Solution

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