1954 AMC 12 Problem 41 — Solution | LIVE by Po-Shen Loh

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1954 AMC 12 Problem 41

Attempt Problem 41 of the 1954 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1954 AMC 12 solutions, or check the answer key.

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41.

The sum of all the roots of $4x^3-8x^2-63x-9=0$ is:

$8$

$2$

$-8$

$-2$

$0$

Answer: B

Concepts:Vieta’s Formulas polynomial

Difficulty rating: 1260

Small Hint:

Use Vieta’s formula for the sum of the roots of a cubic

Big Hint:

Negate the coefficient of $x^2$ and divide by the coefficient of $x^3$

Solution:

For $ax^3+bx^2+\cdots=0,$ the sum of the roots is $-\frac{b}{a}.$ Here it is $-\frac{-8}{4}=2.$

Thus, the correct answer is B.

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Problem 41 in Other Years

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