Let a b be the roots of the equation `x^(2)-kx+k=0` `k in R` .If `a^(2)+b^(2)` is the minimum then find the sum of the roots of the equation

Let a, b be the roots of the equation x^2 - kx + k = 0 , k in R . If a^2 + b^2 is the minimum then find the roots of the equation.

If the product of the roots of the equation x^(2)-5kx+2e^("ln|k|")-1=0 is 49, then the sum of the squares of the roots of the equation is :

If lambda in R is such that the sum of the cubes of the roots of the equation x^(2)+(2-lambda)x+(10-lambda)=0 is minimum then the magnitude of the difference of the roots of this equation is :

if k>0 and the product of the roots of the equation x^(2)-3kx+2e^(2log k)-1=0 is 7 then the sum of the roots is:

If the roots of the quadratic equation x^(2)-2kx+2k^(2)-4=0 are real,then the range of the values of k is

If the product of the roots of the equation x^(2)-3kx+2e^(2ln k)-1=0 is 7 then the roots of the equation are real for k equal to

If the product of the roots of the equation x^(2)-3kx+2e^(2log k)-1=0 is 17 then k=