If a, b are the roots of the equation $x^{2} + x + 1 = 0,$ $t h e n a^{2} + b^{2} =$

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Solution

The correct option is C
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$Given equation: x^{2} + x + 1 = 0 Also, a and b are the roots of the given equation Sum of the roots = a + b = \frac{- c o e f f i c i e n t o f x}{c o e f f i c i e n t o f x^{2}} = - \frac{1}{1} = - 1 Product of the roots ab = \frac{- c o e f f i c i e n t t e r m}{c o e f f i c i e n t o f x^{2}} = \frac{1}{1} = 1 ∴ (a + b)^{2} = a^{2} + b^{2} + 2 a b \Rightarrow 1 - 2 = a^{2} + b^{2} \Rightarrow a^{2} + b^{2} = - 1$

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