Find the value of a for which the sum of the squares of the roots of the equation `x^(2) - ( a - 2) -x - a - 1 = 0` assumes the least value.

The value of a so that the sum of the squares of roots of the equation x^2-(a-2)x-a+1=0 assume the least value is

The value of k for which the sum of the squares of the roots of 2x^(2)-2(k-2)x-k=0 is least is

Find the value of m for which the sum of the roots of the equation 5x^2-4x+2+m(4x^2-2x-1)=0 is 6.

The value of 'p' for which the sum of the square of the roots of 2x^2-2(p-2)x-p-1=0 is least, is

The values of lambda such that sum of the squares of the roots of the quadratic equation x^(2) + (3 - lambda) x + 2 = lambda has the least value is

The least value of |a| for which tan theta and cot theta are the roots of the equation x^(2)+ax+b=0

Find the sum of and product of the roots of the equation 3x ^2 +2x -1=0 .

The value of a for which twice the sum of the cubes of the roots of the equation a=(x^(2)-3)/(x-2) attains its minimum value is (where, a in[0, pi] )

If the roots of the equation x^(2)-4x-log_3 a=0 , are real , the least value of a is :

Find the value of p for which the roots of the equation p x(x-2)+6=0, are equal.