Let r 1 and r 2 be the roots of (x) = ax 2 2x +

Let r₁ and r₂ be the roots of ƒ(x) = ax² − 2x + 20. Observe that ƒ “approaches” the linear function L(x) = −2x + 20 as a → 0. Because r = 10 is the unique root of L, we might expect one of the roots of ƒ to approach 10 as a → 0 (Figure 2). Prove that the roots can be labeled so that

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lim ri a-0 10 and lim 12 = ∞0. a-0