6.The roots of the equation `(a-b+c)x^(2)+4(a-b)x+(a-b-c)=0` are

If a+b+c=0 and a,b,c are rational. Prove that the roots of the equation (b+c-a)x^(2)+(c+a-b)x+(a+b-c)=0 are rational.

Assertion (A): The roots of the equation a(b-c)x^(2)+b(c-a)x+c(a-b)=0 are 1, (c(a-b))/(a(b-c)) Reason (R): If a+b+c=0 then the roots of ax^(2)+bx+c=0 are 1, (c)/(a)

The roots of the equation (b-c) x^2 +(c-a)x+(a-b)=0 are

The roots of the equation a(b-2c)x^(2)+b(c-2a)x+c(a-2b)=0 are, when ab+bc+ca=0

If b is the harmonic mean of a and c and alpha, beta are the roots of the equation a(b-c)x^(2) + b(c-a) x+ c(a-b)=0 , then

If a,b,c are in A.P. then the roots of the equation (a+b-c)x^2 + (b-a) x-a=0 are :

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal, then prove that 2b=a+c .

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal, then prove that 2b=a+c

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal then a,b,c will be in

If a lt c lt b then the roots of the equation (a−b)x^2 +2(a+b−2c)x+1=0 are