If one real root of the quadratic equation 81x² + kx + 256 = 0 is cube of the other root, then a value of k is

The value of $$\lambda $$ such that sum of the squares of the roots of the quadratic equation, x² + (3 – $$\lambda $$)x + 2 = $$\lambda $$ has the least value is -

Consider the quadratic equation (c – 5)x² – 2cx + (c – 4) = 0, c $$ \ne $$ 5. Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the number of elements in S is -

If both the roots of the quadratic equation x² $$-$$ mx + 4 = 0 are real and distinct and they lie in the interval [1, 5], then m lies in the interval :