The quadratic equatin `(2x-a)(2x-c)+lamda(x-2b)(x-2d)=0`, (where `0lt4alt4bltclt4d)` has (A) a root between 2 b and 2d for all `lamda` (B) as root between b nd d for all `-velamda` (C) a root between b and d for all `+velamda` (D) none of these

If a

If a

If altbltcltd then show that the quadratic equation mu(x-a)(x-c)+lamda(x-b)(x-d)=0 has real roots for all real mu and lamda

If ((x-a)(x-b))/((x-c)(x-d)^(2))>=0; where a>b>c>=d>0, then x in

If the two equation x^(2)-cx+d=0 and x^(2)-ax+b=0 have one common root and the second has equal roots then 2(b + d) is equal to

Number of real roots of equation f(x)=0 is (A) 0 (B) 1 (C) 2 (D) none of these

If a,b,c are positive rational numbers such that agtbgtc and the quadratic eqution (a+b-2c)x^2+(b+c-2a)x+(c+a-2b)=0 has a root of the interval (-1,0) then (A) c+alt2b (B) the roots of the equation are rational (C) the roots of are imaginary (D) none of these