If `altbltcltd ,`="" then="" the="" roots="" of="" equation="" `(x-a)(x-c)+2(x-b)(x-d)="0`" are="" real="" and="" distinct.="" (1984,="" 1m)

If a

Prove that both the roots of the equation (x-a)(x-b)+ (x-b)(x-c)+(x-a)(x-c)=0 are real.

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 a , b , c , are real, then prove that roots of the equation 1/(x-a) + 1/(x-b) + 1/(x-c) = 0 are real.

If a

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.

If a ,b ,c ,d are four consecutive terms of an increasing A.P., then the roots of the equation (x-a)(x-c)+2(x-b)(x-d)=0 are a. non-real complex b. real and equal c. integers d. real and distinct