Difference between revisions of "1958 AHSME Problems/Problem 10"
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==Problem== | ==Problem== | ||
− | For what real values of <math> k</math>, other than <math> k | + | For what real values of <math> k</math>, other than <math> k = 0</math>, does the equation <math> x^2 + kx + k^2 = 0</math> have real roots? |
<math> \textbf{(A)}\ {k < 0}\qquad | <math> \textbf{(A)}\ {k < 0}\qquad |
Latest revision as of 03:02, 29 June 2017
Problem
For what real values of , other than , does the equation have real roots?
Solution
An expression of the form has at least one real root when .
Substituting for and for , we have
but the range of is , so the answer is
See also
1958 AHSC (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 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
All AHSME Problems and Solutions |
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