Difference between revisions of "1974 AHSME Problems/Problem 10"
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+ | ==Problem== | ||
+ | <!-- don't remove the following tag, for PoTW on the Wiki front page--><onlyinclude>What is the smallest integral value of <math> k </math> such that | ||
+ | <cmath> 2x(kx-4)-x^2+6=0 </cmath> | ||
+ | has no real roots?<!-- don't remove the following tag, for PoTW on the Wiki front page--></onlyinclude> | ||
+ | |||
+ | <math> \mathrm{(A)\ } -1 \qquad \mathrm{(B) \ }2 \qquad \mathrm{(C) \ } 3 \qquad \mathrm{(D) \ } 4 \qquad \mathrm{(E) \ }5 </math> | ||
==Solution== | ==Solution== | ||
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==See Also== | ==See Also== | ||
{{AHSME box|year=1974|num-b=9|num-a=11}} | {{AHSME box|year=1974|num-b=9|num-a=11}} | ||
+ | [[Category:Introductory Algebra Problems]] | ||
+ | {{MAA Notice}} |
Latest revision as of 17:14, 18 November 2015
Problem
What is the smallest integral value of such that
has no real roots?
Solution
Expanding, we have , or
. For this quadratic not to have real roots, it must have a negative discriminant. Therefore,
. From here, we can easily see that the smallest integral value of
is
.
See Also
1974 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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 | ||
All AHSME Problems and Solutions |
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