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

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 dot

If a gt 0 and b^(2) - 4 ac = 0 then solve ax^(3) + (a + b) x^(2) + (b + c) x + c gt 0 .

Prove that 2/(b+c)+2/(c+a)+2/(a+b) 0.

If the expression a(b-c)x^(2)+b(c-a)xy+c(a-b)y^(2) is a perfect square, then a,b,c are in

If a ,b ,c are non zero (a b c^2)x^2+3a^2c x+b^2c x-6a^2-a b+2b^2=0 are rational.

Solve |(x+a,b,c),(a,x+b,c),(a,b,x+c)|=0

If a ,b ,c in R such that a+b+c=0a n da!=c , then prove that the roots of (b+c-a)x^2+(c+a-b)x+(a+b-c)=0 are real and distinct.

In any /_\ A B C , prove that (b^2-c^2)cotA+(c^2-a^2)cotB+(c^a-b^2)cotC=0