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Calculus and Beyond Homework Help
The Intersection of Tangent Lines: Finding the Range of C
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[QUOTE="Let'sthink, post: 5497193, member: 563429"] The equation of curve is y = x⁴ + cx³ +12x² -5x +2. Let the line be y = mx +d. The x coordinate of the points of intersection will satisfy the equation mx + d = x⁴ + cx³ +12x² -5x +2 or x⁴ + cx³ +12x² -(5+m)x + (2-d) = 0. This equation must have four distinct real roots. If α, β, γ and δ are the real distinct roots then we have α + β + γ + δ = - c ----------------- (1) αβ + βγ + γδ + δα = 12 ---------- (2) αβγ + βγδ + γδα + δαβ = 5+m -----(3) and αβγδ = 2-d ------------------------ (4) There are 3 unknowns and 4 equations and we need to find only the value of c. [/QUOTE]
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Calculus and Beyond Homework Help
The Intersection of Tangent Lines: Finding the Range of C
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