Limit of sequence of real polynomials in one variable $\lambda$ of degree d, restricted to $\lambda \geq 0$.

Question

I'm reading the following proposition and proof:

Proof:

I'm having two questions:

1. Is the first part marked in red supposed to show that such $a_0,...,a_d$ exist and indeed could be computed with Cramer's rule?

2. How is that first part marked in red related to the second part marked in red? What's the line of reasoning here?