Difference between revisions of "1960 AHSME Problems/Problem 1"
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If <math>2</math> is a solution (root) of <math>x^3+hx+10=0</math>, then <math>h</math> equals: | If <math>2</math> is a solution (root) of <math>x^3+hx+10=0</math>, then <math>h</math> equals: | ||
| − | <math>\textbf{(A)}10\qquad \textbf{(B )}9 \qquad \textbf{(C )}2\qquad \textbf{(D )}-2\qquad \textbf{(E )}-9</math> | + | <math>\textbf{(A) }10\qquad \textbf{(B) }9 \qquad \textbf{(C) }2\qquad \textbf{(D) }-2\qquad \textbf{(E) }-9</math> |
==Solution== | ==Solution== | ||
| − | Substitute <math>2</math> for <math>x</math>. We are given that this equation is true. | + | Substitute <math>2</math> for <math>x</math>. We are given that this equation is true. Thus, |
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| + | <math>2^3+2h+10 =0</math> | ||
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| + | <math>18+2h=0</math> | ||
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| + | <math>2h=-18</math> | ||
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| + | <math>h=-9</math> | ||
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| + | Thus, the answer is <math>\boxed{\textbf{(E) }-9}</math>. | ||
==See Also== | ==See Also== | ||
| − | {{AHSME 40p box|year=1960 |before=[[1959 AHSME]]| | + | {{AHSME 40p box|year=1960|before=[[1959 AHSME]]|num-a=2}} |
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| + | [[Category:Introductory Algebra Problems]] | ||
Latest revision as of 13:32, 5 June 2024
Problem
If 
is a solution (root) of 
, then 
equals:
Solution
Substitute for 
. We are given that this equation is true. Thus,
Thus, the answer is 
.
See Also
| 1960 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by 1959 AHSME |
Followed by Problem 2 | |
| 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 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
| All AHSME Problems and Solutions | ||
