If the set of all a R - 1 , for which the roots of the equation (1-a) x^2+2(a-3) x+9=0 are positive is (- ,- ] [ , ) , then 2 + + is equal to _______ .

Step-by-step solution

Both the roots are positive aligned & D 0 & 4(a-3)^2-4 9(1-a) 0 & a^2-6 a+9-9+9 a 0 & a^2+3 a 0 & a(a+3) 0 aligned a (- ,-3] [0, ) ...(i) aligned & - b 2 a 0 & 2( a -3) 2( a -1) 0 aligned a (- , 1) (3, ) ...(ii) f(0)=9 0 Equation (i) (ii) aligned & a (- ,-3] [0,1) & 2 + + -6+0+1=7 aligned