Three Secants of a Cubic

★ 7/10algebra Polynomials analytic geometry Vieta's Formulas

Problem

The graph of a cubic function $f(x)$ passes through the points $A(2, 4)$ , $B(3, 9)$ , $C(4, 16)$ . Lines $AB$ , $AC$ , $BC$ meet the graph of $f(x)$ again at points $D$ , $E$ , $F$ respectively, and the $x$ -coordinates of $D, E, F$ sum to $24$ . Find $f(0)$ .

Answer

Solution

Difficulty	7/10
Topics	algebra, Polynomials, analytic geometry, Vieta's Formulas

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