Find the sum and the product of the roots of the following equation.

x² – 6x + 5 = 0

Show that the roots of the equation

(x – a) (x – b) + (x – b) (x – c) + (x – c) (x – a) = 0 are always real and they cannot be unless a = b = c.

If the equation (1 + m²) x² + 2mcx + c² – a² = 0 has equal roots, then prove that c² = a² (1 + m²)

Find the sum and the product of the roots of the following equation.

kx² + ax + pk = 0

Find the sum and the product of the roots of the following equation.

3x² – 5x = 0