MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2009 National Olympiad First Round
19
19
Part of
2009 National Olympiad First Round
Problems
(1)
roots of two quadratic equation
Source: 0
4/28/2009
a
a
a
is a real number.
x
1
x_1
x
1
and
x
2
x_2
x
2
are the distinct roots of x^2 \plus{} ax \plus{} 2 \equal{} x.
x
3
x_3
x
3
and
x
4
x_4
x
4
are the distinct roots of (x \minus{} a)^2 \plus{} a(x \minus{} a) \plus{} 2 \equal{} x. If x_3 \minus{} x_1 \equal{} 3(x_4 \minus{} x_2), then x_4 \minus{} x_2 will be ?
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a
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a
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2
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3
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None
<span class='latex-bold'>(A)</span>\ \frac {a}{2} \qquad<span class='latex-bold'>(B)</span>\ \frac {a}{3} \qquad<span class='latex-bold'>(C)</span>\ \frac {2a}{3} \qquad<span class='latex-bold'>(D)</span>\ \frac {3a}{2} \qquad<span class='latex-bold'>(E)</span>\ \text{None}
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2
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3
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3
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2
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E
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None
quadratics