If the sum of the roots of an equation is 2 and the sum of their cubes is 98, then find the equation.

If sum of the roots of quadratic equations is 10 and the product is 9, then form the quadratic equation:

Consider the graph of y = f(x) as shown in the following figure. (i) Find the sum of the roots of the equation f (x) = 0. (ii) Find the product of the roots of the equation f(x) = 4. (iii) Find the absolute value of the difference of the roots of the equation f(x) = x+2 .

The sum of the squares of the first n natural numbers is 285, while the sum of their cubes is 2025. Find the values of n.

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.

A quadratic equation with integral coefficients has two different prime numbers as its roots. If the sum of the coefficients of the equation is prime, then the sum of the roots is 2 b. 5 c. 7 d. 11

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 and product of the roots of the equation ax^(2)-5x+c=0 are both equal to 10 then find the values of a and c.

If alpha and beta are the roots of the equation ax^(2)+bx+c=0 then the sum of the roots of the equation a^(2)x^(2)+(b^(2)-2ac)x+b^(2)-4ac=0 is

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.