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# Algebra

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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

#1
+14441
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What is the value of k?

Hello Guest!

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

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

May 11, 2022