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[Solved] Equations roots

 
Quadratic Equations
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June 15, 2021 11:33 am
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(@armor)
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If the equation x^2-kx-4=0 has two positive roots, find the range of k.

 

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June 15, 2021 11:34 am
Topic starter
Staff 
(@armor)
Admin
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The condition of two positive roots (denoted by \small x_{1},x_{2}) implies

 \small x_{1}+x_{2}=k>0,

\small x_{1}x_{2}=k^2-4>0,

\small \Delta =k^2-4(k^2-4)=-3k^2+16\geq 0.

From these three inequalities, we can easily obtain \small 2<k\leq 4\sqrt{3}/3.

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