Question

If a, b are the roots of the equation \[x^2 + x + 1 = 0, \text { then } a^2 + b^2 =\]

Options

• 1

• 2

• -1

• 3

Answer 1

−1
Given equation: 

\[x^2 + x + 1 = 0\]

Also, 

\[a\] and \[b\] are the roots of the given equation.
Sum of the roots = \[a + b = \frac{- \text { Coefficient of }x}{\text { Coefficient of } x^2} = - \frac{1}{1} = - 1\]

Product of the roots = \[ab = \frac{\text { Constant term }}{\text { Coefficient of } x^2} = \frac{1}{1} = 1\]

\[\therefore (a + b )^2 = a^2 + b^2 + 2ab\]

\[ \Rightarrow ( - 1 )^2 = a^2 + b^2 + 2 \times 1\]

\[ \Rightarrow 1 - 2 = a^2 + b^2 \]

\[ \Rightarrow a^2 + b^2 = - 1\]