Let a, b, c be three non-zero real numbers such that the equation 3 a x+2 b x=c , x [- 2 , 2 ] has two distinct real roots and with + = 3 . Then the value of b a is

Step-by-step solution

and are roots of 3 a x+2 ~b x= c aligned & 3 a +2 b =c ...(i) & 3 a +2 b =c...(ii) aligned Subtracting (ii) from (i), we get aligned & 3 a( - )+2 b( - )=0 & aligned & 3 a[ .-2 ( + 2 ) ( - 2 ) ] &++2 b [2 ( + 2 ) ( - 2 ) ]=0 & - 3 a [2 ( 6 ) ( - 2 ) ] &++2 b [2 ( 6 ) ( - 2 ) ]=0 aligned aligned aligned & - 3 a ( - 2 )+2 b [ 3 ( - 2 ) ]=0 & - 3 a+2 3 b=0 b a = 1 2 =0.5 aligned