Question

If a and b are roots of the equation \[x^2 - x + 1 = 0\],  then write the value of a² + b².

Answer 1

Given: 

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

Also, 

\[a \text { and } b\] are the roots of the equation.
Then, sum of the roots = \[a + b = - \left( \frac{- 1}{1} \right) = 1\]

Product of the roots = \[ab = \frac{1}{1} = 1\]

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

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

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

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