Find the quadratic equation whose sum of the roots of is 2 and sum of their cubes is 98.

Find four numbers in an A.P whose sum is 20 and sum of their squares is 120 .

The quadratic equation whose roots are three times the roots of the equation 2x^(2)+3x+5=0 , is

Consider the quadratic equation x^2+x+1=0 .If the two roots of the given quadratic are alpha and beta .Show that alpha^2=beta

Find two positive numbers such that their sum is 8 and the sum of their squares is minimum.