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# Let f be a function for which f(x/3) = x^2 + x + 1. Find the sum of al

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Math Expert
Joined: 02 Sep 2009
Posts: 59725
Let f be a function for which f(x/3) = x^2 + x + 1. Find the sum of al  [#permalink]

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18 Mar 2019, 01:35
00:00

Difficulty:

75% (hard)

Question Stats:

37% (02:25) correct 63% (02:39) wrong based on 19 sessions

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Let f be a function for which f(x/3) = x^2 + x + 1. Find the sum of all values of $z$ for which f(3z) = 7.

(A) -1/3
(B) -1/9
(C) 0
(D) 5/9
(E) 5/3

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Concentration: Finance, Marketing
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Re: Let f be a function for which f(x/3) = x^2 + x + 1. Find the sum of al  [#permalink]

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19 Mar 2019, 11:12
Put x/3 = 3z
x = 9z in the equation.

$$81z^2+9z+1 = 7$$
$$81z^2+9z-6 = 0$$
$$or 27z^2+3z-2 = 0$$
Sum = -b/a
b = 3
a = 27
sum = -3/27 = -1/9

Re: Let f be a function for which f(x/3) = x^2 + x + 1. Find the sum of al   [#permalink] 19 Mar 2019, 11:12
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