The problem I'm struggling with is:
If a and b are real numbers such that a + b is not equal to 0 and b is not equal to 0:
(a) Show that if there is only one real root of the equation x^2 + ax + b = 0 where 0 < x < 1, then b(a + b + 1) < 0.
(Hint: Let f(x) = x^2 + ax + b.
(b) Hence, or otherwise, prove that the following equation 1/(x+2) + a/(x+1) + b/x = 0 has two distinct real roots only one of which is positive.
Could someone please please explain to me how to solve this problem?