If sum of the roots of `ax^(2)+bx+c=0` is equal to the sum of the squares of their reciprocals then show that `2a^(2)c=ab^(2)+bc^(2)`.

If the sum of the roots of x^(2) + bx + 1 = 0 , is equal to the sum of their squares, then b =

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

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 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.

The sum of the roots of the quadratic equation ax^(2) + bx + c = 0 is equal to the sum of the squares of their recipocals, prove that (c)/(a),(a)/(b),(b)/(c) are in A.P.

For given equation x^(2) -ax+b=0 , match conditions in column I with possible values in column II {:("column -I " , "Colum-II"),("(A) If roots differ by unity then " a^(2)" is equal to" , "(p) b(ab+2)"),("(B) If roots differ by unity then " 1 + a^(2) " is equal to " , "(q) 1 + 4b"),("(C) If one of the root be twice the other then " 2a^(2) " is equal to " , "(r) 2(1+2b)"),("(D) If the sum of roots of the equation equal to the sum of squares of their reciprocal then " a^(2) " is equal to " , "(s) 9b"):}

If the sum of the rotsof the equation px^2+qx+r=0 be equal to the sum of their squares, show that 2pr=pq+q^2

If the ratio of the roots of the equation ax^(2)+bx+c=0 is m: n then

If the roots of the equation ax^(2)+bx+c=0 are in the ratio m:n then