A Ratio Pinned by a Parabola

★ 7/10functions Quadratic Equations algebra inequality Casework Discriminant

Problem

The quadratic $f(x) = ax^2 + 2bx + c$ with $c > b > a$ passes through $(1, 0)$ and meets the line $y = -a$ . Prove that

0 \le \frac{b}{a} < 1.

Answer

Solution

Difficulty	7/10
Topics	functions, Quadratic Equations, algebra, inequality, Casework, Discriminant

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