Difference between revisions of "1954 AHSME Problems/Problem 41"
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== Solution 1 == | == Solution 1 == | ||
− | By Vieta's Formulas, <math>\frac{--8}{4}=2</math>, <math>\fbox{ | + | By Vieta's Formulas, <math>\frac{--8}{4}=2</math>, <math>\fbox{B}</math> |
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== Solution 2 == | == Solution 2 == | ||
<math>4x^3-8x^2-63x-9=0</math> | <math>4x^3-8x^2-63x-9=0</math> | ||
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We can see that the negative sum of the roots is the coefficient of the <math>x^2</math> term, <math>-2</math>. | We can see that the negative sum of the roots is the coefficient of the <math>x^2</math> term, <math>-2</math>. | ||
− | So the actual sum of the roots is <math>-(-2)</math>, or <math>2 \implies \fbox{ | + | So the actual sum of the roots is <math>-(-2)</math>, or <math>2 \implies \fbox{B}</math> |
Latest revision as of 00:02, 14 November 2019
Problem 41
The sum of all the roots of is:
Solution 1
By Vieta's Formulas, ,
Solution 2
By Vieta's Formulas:
We can see that the negative sum of the roots is the coefficient of the term, . So the actual sum of the roots is , or