An algebra problem by Sandeep Bhardwaj

Algebra Level 4

If \(A_0(x),A_1(x), \text{ and } A_2(x)\) are the three polynomials and \(a_0,a_1,\text{ and } a_2\) are three distinct real numbers, then compute \[A_0(x)+A_1(x)+A_2(x).\]

\[A_0(x)=\dfrac{(x-a_1)(x-a_2)}{(a_0-a_1)(a_0-a_2)} ,\quad A_1(x)=\dfrac{(x-a_0)(x-a_2)}{(a_1-a_0)(a_1-a_2)}, \\ A_2(x)=\dfrac{(x-a_0)(x-a_1)}{(a_2-a_0)(a_2-a_1)} , \quad A(x)=(x-a_0)(x-a_1)(x-a_2)\]

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