Question 1118008
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<U>Answer</U>.  &nbsp;&nbsp;The roots are &nbsp;-3 &nbsp;and &nbsp;-1.  &nbsp;The value of &nbsp;k&nbsp; is &nbsp;6.



<U>Solution</U>


<pre>
The equation is equivalent to  


{{{x^2 + 4x + k/2}}} = 0.


So, the sum of the roots is -4 (the Vieta's theorem) and their ratio is 3.


From it, you get  the roots values  -3 and -1  (mentally).


The value of {{{k/2}}} is the product of the roots  (-3)*(-1) = 3  (the Vieta's theorem).  Hence, k = 2*3 = 6.
</pre>

Solved.


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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Using-Vieta%27s-theorem-to-solve-qudratic-equations.lesson>Using Vieta's theorem to solve qudratic equations and related problems</A>

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