Let 6 a 4 ~b 3 c then the equation (2 x - a )(3 x - b )+(3 x - b )(4 x - c )+(4 x - c )(2 x - a )=0 has

Step-by-step solution

Let f(x)=(2 x-a)(3 x-b)+(3 x-b)(4 x-c)+(4 x-c)(2 x-a)=0f ( a 2 )= ( 3 a 2 -b )(2 a-c) 0 since a 2 b 3 c 4 f ( b 3 )= ( 4 b 3 -c ) ( 2 b 3 -a ) 0 Since f ( a 2 ) f ( b 3 ) 0 one real root between ( a 2 , ~b 3 ) Both roots are real Equation is quadratic in nature Also, f ( c 4 ) 0 f ( b 3 ) f ( c 4 ) 0 other between ( b 3 , c 4 )