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

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

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

If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, show that 2//b=1//a+1// c dot

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 the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, show that 2//b=1//a+1//cdot

Column I, Column II If a ,b ,c ,a n dd are four zero real numbers such that (d+a-b)^2+(d+b-c)^2=0 and he root of the equation a(b-c)x^2+b(c-a)x=c(a-b)=0 are real and equal, then, p. a+b+c=0 If the roots the equation (a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0 are real and equal, then, q. a ,b ,ca r einAdotPdot If the equation a x^2+b x+c=0a n dx^3-3x^2+3x-0 have a common real root, then, r. a ,b ,ca r einGdotPdot Let a ,b ,c be positive real number such that the expression b x^2+(sqrt((a+b)^2+b^2))x+(a+c) is non-negative AAx in R , then, s. a ,b ,ca r einHdotPdot

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 equation a(b-c)x^2+b(c-a)x+c(a-b)=0 be equal prove that a,b,c are in H.P.

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