Let a ,   b ,   c ,   d be distinct real numbers such that a ,   b are roots of x 2 - 5 c x - 6 d = 0 , and c ,   d are roots of x 2 - 5 a x - 6 b = 0 . Then b + d is

Step-by-step solution

It is given that the quadratic equation x 2 - 5 c x - 6 d = 0 has roots a and b, then a + b = 5 c  and  a b = - 6 d and, the quadratic equation x 2 - 5 a x - 6 b = 0 has roots C and d, then c + d = 5   a and c d=-6 b Now, from Eqs. (i) and (iii), we have Now, from Eqs. (i) and (iii), we have ( a + b ) − ( c + d ) = 5 c − 5 a ⇒ ( a − c ) + ( b − d ) = − 5 ( a − c ) ⇒ ( b − d ) = 6 ( c − a ) ∴ a and c are the roots of equations. x 2 - 5