If a and b are the roots of $x^{2} - a x + b^{2} = 0,$ then $a^{2} + b^{2} =$

2 a^{2} - b^{2}

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a^{2} + b^{2}

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a^{2} - 2 b^{2}

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a^{2} - b^{2}

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Solution

The correct option is B $a^{2} - 2 b^{2}$
Given equation is
$x^{2} - a x + b^{2} = 0.... (1)$
since $a, b$ are roots for equation (1)
Then sum of roots $a + b = a$
Products of roots $a . b = b^{2}$
consider ${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$
$\Rightarrow$ $a^{2} = a^{2} + b^{2} + 2 b^{2}$
$\Rightarrow$ $a^{2} + b^{2} = a^{2} - 2 b^{2}$

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