MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1956 AMC 12/AHSME
23
23
Part of
1956 AMC 12/AHSME
Problems
(1)
Zero Discriminant
Source:
2/15/2009
About the equation ax^2 \minus{} 2x\sqrt {2} \plus{} c \equal{} 0, with
a
a
a
and
c
c
c
real constants, we are told that the discriminant is zero. The roots are necessarily:
<
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(
A
)
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equal and integral
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(
B
)
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equal and rational
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(
C
)
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equal and real
<span class='latex-bold'>(A)</span>\ \text{equal and integral} \qquad<span class='latex-bold'>(B)</span>\ \text{equal and rational} \qquad<span class='latex-bold'>(C)</span>\ \text{equal and real}
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(
A
)
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equal and integral
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(
B
)
<
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equal and rational
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(
C
)
<
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equal and real
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(
D
)
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equal and irrational
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(
E
)
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equal and imaginary
<span class='latex-bold'>(D)</span>\ \text{equal and irrational} \qquad<span class='latex-bold'>(E)</span>\ \text{equal and imaginary}
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(
D
)
<
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equal and irrational
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(
E
)
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equal and imaginary
calculus
integration