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 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 the equation |x^2+b x+c|=k has four real roots, then a. b^2-4c > 0 and 0 0 and k > (4c-b^2)/4 d. none of these

If the equation |x^2+b x+c|=k has four real roots, then a. b^2-4c > 0 and 0 0 and k > (4c-b^2)/4 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

lf 0 < a < b < c < d , then the quadratic equation ax^2 + [1-a(b+c)]x+abc-d=0 A) Real and distinct roots out of which one lies between c and d B) Real and distinct roots out of which one lies between a and b C) Real and distinct roots out of which one lies between b and c (D) non -real roots

lf 0 < a < b < c < d, then the quadratic equation ax^2 + [1-a(b+c)]x+abc-d=0 A) Real and distinct roots out of which one lies between c and d B) Real and distinct roots out of which one lies between a and b C) Real and distinct roots out of which one lies between b and c (D) non -real roots

If a lt b lt c lt d then show that (x-a)(x-c)+3(x-b)(x-d)=0 has real and distinct roots.

If a lt b lt c lt d then show that (x-a)(x-c)+3(x-b)(x-d)=0 has real and distinct roots.