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

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

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 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.

Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7),(7,3,7)]=[0,0,0] Let b=6, with a and c satisfying (E). If alpha and beta are the roots of the quadratic equation ax^2+bx+c=0 then sum_(n=0)^oo (1/alpha+1/beta)^n is (A) 6 (B) 7 (C) 6/7 (D) oo

If alpha" and "beta are the solutions of the quadratic equation ax^(2)+bx+c=0 such that beta= alpha^(1/3) , then

If the roots of the quadratic equation ax^(2) + cx + c = 0 are in the ratio P : q then show that sqrt (p/q) + sqrt (q/p) + sqrt (c/a) = 0