Consider the quadratic equation nx^(2) +...

Consider the quadratic equation `nx^(2) +7 sqrt(nx)+n=0`, where n is a positive intergar. Which of the following statements are necessarliy correct ?
I. For any n, the roots are distinct.
(II) There are infinitely many values of n for which both roots are real.
(III) The product of the roots is necessarlity an integer.

Similar Questions

Explore conceptually related problems

If the roots of quadratic equations are real and distinct then which of the following is correct ?

Find the value of K for which the quadratic equation kx^(2)+2x+1=0, has real and distinct root.

If the roots of the quadratic equation x^(2) - 4x- log_(10) N= 0 are all real, then the minimum value of N is

If m and n are the roots of the quadratic equation x^(2) + px + 8=0 with m- n = 2, then the value of p' is

If roots of the quadratic equation x^(2) + Nx - 444N=0 are integers and N is a prime number then number of possible values of N is

Find the condition that one root of the quadratic equation ax^(2)+bx+c=0 shall be n times the other, where n is positive integer.