As D approaches zero

Calculus Level 4

\[\large f_k(x) = A(k)x^2 + B(k)x + C(k),\] Let \(k\) be a real parameter and \(A\), \(B\) and \(C\) are real, continuous functions on \(\mathbb R\).

Suppose that for a certain interval \(k \in \langle p, q \rangle\), the equation \(f_k(x) = 0\) has two real solutions; but at the end of the interval, \(f_q(x) = 0\) does not have two real solutions.

What more can you say about the solutions of \(f_q(x) = 0\)?

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