Without solving, examine the nature of roots of the given quadratic equation:

$9x^2-6x+1=0$

 

Without solving, examine the nature of roots of the given quadratic equation:

$x^2+x+2=0$

Without solving, examine the nature of roots of the given quadratic equation:

$25x^2-25x+6=0$

Without solving, examine the nature of roots of the given quadratic equation:

$x^2-3x+1=0$

Without solving, examine the nature of roots of the given quadratic equation:

$3x^2-10x+3=0$

Without solving, examine the nature of roots of the given quadratic equation:

$x^2-x+1=0$

Without solving, find the sum and the product of the roots of the given quadratic equation.

$x^2-3x-3=0$

Without solving, find the sum and the product of the roots of the given quadratic equation.

$5x^2-10x+2=0$

Without solving, find the sum and the product of the roots of the given quadratic equation.

$2x^2-3\sqrt{3}x+3=0$