If p, q, r are + ve and are on A.P., the roots of quadratic equation $$p{x^2} + qx + r = 0$$ are all real for

The number of points of intersection of two curves y = 2 sin x and y $$ = 5{x^2} + 2x + 3$$ is

Let $$\alpha \,,\,\beta $$ be the roots of the equation (x - a) (x - b) = c, $$c \ne 0$$. Then the roots of the equation $$(x - \alpha \,)\,(x - \beta ) + c = 0$$ are

The product of $$n$$ positive numbers is unity. Then their sum is