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Difference between revisions of "2019 AMC 12A Problems/Problem 17"

(Created page with "==Problem== Let <math>s_k</math> denote the sum of the <math>\textit{k}</math>th powers of the roots of the polynomial <math>x^3-5x^2+8x-13</math>. In particular, <math>s_0=3...")
 
m (→‎Solution)
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==Solution==
 
==Solution==
 +
Applying Newton Sums we get the answer as 10
  
 
==See Also==
 
==See Also==

Revision as of 18:16, 9 February 2019

Problem

Let $s_k$ denote the sum of the $\textit{k}$th powers of the roots of the polynomial $x^3-5x^2+8x-13$. In particular, $s_0=3$, $s_1=5$, and $s_2=9$. Let $a$, $b$, and $c$ be real numbers such that $s_{k+1} = a \, s_k + b \, s_{k-1} + c \, s_{k-2}$ for $k = 2$, $3$, $....$ What is $a+b+c$?

$\textbf{(A)} \; -6 \qquad \textbf{(B)} \; 0 \qquad \textbf{(C)} \; 6 \qquad \textbf{(D)} \; 10 \qquad \textbf{(E)} \; 26$

Solution

Applying Newton Sums we get the answer as 10

See Also

2019 AMC 12A (Problems • Answer Key • Resources)
Preceded by
Problem 16 		Followed by
Problem 18
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 12 Problems and Solutions

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