If `a b+b c+c a=0,` then solve `a(b-2c)x^2+b(c-2a)x+c(a-2b)=0.`

If a , b , c are positive numbers such that a gt b gt c and the equation (a+b-2c)x^(2)+(b+c-2a)x+(c+a-2b)=0 has a root in the interval (-1,0) , then

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

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 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.

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

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

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