i) The discriminant is
, so the roots are real
ii) The equation is
2) The equation is
If the roots are equal then the discriminant is 0.
How do i prove these?
1) If a, b and c are real, show that the roots of the following equations are real:
(i) (b+c)x^2 - (a + b + c)x + a = 0
(ii) (a + b)(x^2 + 5x + 1) = c(x^2-1)
2) 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.
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.