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The nonzero roots of the equation x^2 + 6k + x = 0 are in the ratio \(2:7\). What is the value of k?

 May 11, 2022
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What is the value of k?

 

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\(x^2 +x+ 6k = 0\\ x= -0.5\pm \sqrt{0.25-6k}\)

\((-0.5-\sqrt{0.25-6k}):(-0.5+ \sqrt{0.25-6k})=2:7\\ -3.5-7\sqrt{0.25-6k}=-1+2\sqrt{0.25-6k}\\ -2.5=9\sqrt{0.25-6k}\\ 6.25=20.25-486k\\ 486k=14\\ \color{blue}k=\dfrac{7}{243}=0. 0288\)
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 May 11, 2022

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