If $ \alpha $ and $ \beta $ are the roots of $ x^{2}-a x+b^{2}=0 $, then $ \alpha^{2}+\beta^{2} $ is equal to

Question

If $ \alpha $ and $ \beta $ are the roots of $ x^{2}-a x+b^{2}=0 $, then $ \alpha^{2}+\beta^{2} $ is equal to, $ a^{2}-2 b^{2} $, $ 2 a^{2}-b^{2} $, $ a^{2}-b^{2} $, $ a^{2}+b^{2} $

MARKS App · Accepted Answer

Given equation, x 2 − a x + b 2 = 0 → ( 1 ) We know that, sum of the roots is given by α + β = a and the product of the roots is given by α β = b 2 Now, α 2 + β 2 = ( α + β ) 2 − 2 α β = a 2 − 2 b 2

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