Let \( V = \{ p : p(x) = a_0 + a_1 x + a_2 x^2, a_0, a_1, a_2 \in \mathbb{R} \} \) be the vector space of all polynomials of degree at most 2 over the real field \( \mathbb{R} \). Let \( T: V \to V \) be the linear operator given by
\[ T(p) = (p(0) - p(1)) + (p(0) + p(1)) x + p(0) x^2. \] Then the sum of the eigenvalues of \( T \) is \(\underline{\hspace{2cm}}\) .
Let \( V = \{ p : p(x) = a_0 + a_1 x + a_2 x^2, a_0, a_1, a_2 \in \mathbb{R} \} \) be the vector space of all polynomials of degree at most 2 over the real field \( \mathbb{R} \). Let \( T: V \to V \) be the linear operator given by
\[ T(p) = (p(0) - p(1)) + (p(0) + p(1)) x + p(0) x^2. \] Then the sum of the eigenvalues of \( T \) is \(\underline{\hspace{2cm}}\) .
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Correct Answer: 1
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