# The cool name is Cool Symmetry. Part IV

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, and if $$\dfrac{1}{A(x)}=\dfrac{A_0}{x-a_0}+\dfrac{A_1}{x-a_1}+\dfrac{A_2}{x-a_2}$$, then $A_i \text{ (for i=0,1,2) equals : }$

Note : $$A'(y)$$ represents the derivative of $$A(x)$$ at $$x=y$$.

$A_0(x)=\dfrac{(x-a_1)(x-a_2)}{(a_0-a_1)(a_0-a_2)}$ $A_1(x)=\dfrac{(x-a_0)(x-a_2)}{(a_1-a_0)(a_1-a_2)}$ $A_2(x)=\dfrac{(x-a_0)(x-a_1)}{(a_2-a_0)(a_2-a_1)}$ $A(x)=(x-a_0)(x-a_1)(x-a_2)$

×