Thriving Scholars TMUA Full Mock Test 1 Paper 1 · Question 9

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Thriving Scholars TMUA Full Mock Test 1 Paper 1 · Q9

Paper 1Algebra

Let $s_k$ denote the sum of the $k$ 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 $s_{k+1}=as_k+bs_{k-1}+cs_{k-2}$ for $k=2,3,\ldots$ What is $a+b+c$ ?

-6

0

6

10

26

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