Hello people,

How do i prove these?If a, b and c are real, show that the roots of the following equations are real:

1)

(i)(b+c)x^2 - (a + b + c)x + a = 0

(ii)(a + b)(x^2 + 5x + 1) = c(x^2-1)

If roots of the equation (x-a)(x-b) + (x-b)(x-c) + (x-c)(x-a) = 0 are equal, prove that a = b = c.

2)

3)If a = b = c, prove that the roots of the equation:

(x-a)(x-b) + (x-b)(x-c) + (x-c)(x-a) = 0 are equal.