`ab x^2+(b^2-a c)x-b c=0`

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

a,b and c are non-zero distinct real numbers, common root of equations (a-b)x^(2)+(b-c)x+(c-a)=0c(a-b)x^(2)+a(b-c)x+b(c-a)=0 is

Show that the roots of the equation (a^(2)-bc)x^(2)+2(b^(2)-ac)x+c^(2)-ab=0 are equal if either b=0 or a^(3)+b^(3)+c^(3)-3acb=0

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

If a,b and c are in AP and if the equations (b-c)x^(2)+(c-a)x+(a-b)=0 and 2(c+a)x^(2)+(b+c)x+(a-b)=0 have a common root,then

If (a-b)x^(2)+2(b-c)x+(a-c+b)=0 (a,b,c in R) and x^(2)+2x+5=0 have a common root,value of a,b and c