If the sum of the roots of the quadratic equation `a x^2+b x+c=0` is equl to the sum of the squares of their reciprocals, then prove that `a/c , b/a a n d c/b` are in H.P.

If the sum of the roots of the quadratic equation ax^(2)+bx+c=0 is equal to the sum of the squares of their reciprocals, then (a)/(c ), (b)/(a)" and "(c )/(b) are in

If the sum of the roots of the quadratic equation ax^(2) + bx + c = 0 is equal to the sum of the squares of their reciprocals, then prove that 2a^(2)c = c^(2)b + B^(2)a.

If the sum of the roots of the quadratic equation ax^2 + bx + c = 0 ( abc ne 0) is equal to the sum of the squares of their reciprocals, the sum of the squares of their reciprocals, then a/c , b/a , c/b are in H.P.

Show that the sum of roots of a quadratic equation ax^(2)+bx+c=0 (a ne 0) is (-b)/(a) .

If the sum of the roots of the equation 1/(x+a)+1/(x+b)=1//c is zero, the prove that the product of the root is (-1/2)(a^2+b^2)dot

The sum of real roots of the equation |x-2|^2+|x-2|-2=0 is (A) 4 (B) 1 (C) 2 (D) -2

If a ,b and c are in A.P. and one root of the equation a x^2+b c+c=0 is 2 , the find the other root dot

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+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+2c=0 where a ,b ,c in R

The quadratic equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 has equal roots if