# 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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