Let (a) and (a) be the roots of the equation ( [3] 1+a -1) x^2+( 1+a -1) x+( [6] 1+a -1)=0 where a -1 then _ a 0⁺ (a) and _ a 0⁺ (a) respectively are

Step-by-step solution

Let A=1+a When a 0⁺, A 1⁺ Given function is written as aligned & (A^ 1 3 -1 ) x^2+ (A^ 1 2 -1 ) x+ (A^ 1 6 -1 )=0 & ( A^ 1 3 -1 A-1 ) x^2+ ( A^ 1 2 -1 A-1 ) x+ ( A^ 1 6 -1 A-1 )=0 aligned Taking _ x 0⁺ on both sides, we get array ll & 1 3 x^2+ 1 2 x+ 1 6 =0 & 2 x^2+3 x+1=0 & x=-1 or -1 2 array i.e. _ x 0⁺ (a)=-1 and _ x 0⁺ (a)= -1 2