SOLUTION: Find k and the roots if 2x^2+8x+k=0 and the roots are in the ratio 3:1.

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Question 1118008: Find k and the roots if 2x^2+8x+k=0 and the roots are in the ratio 3:1.
Answer by ikleyn(52781) About Me  (Show Source):
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Answer.   The roots are  -3  and  -1.  The value of  k  is  6.


Solution 

The equation is equivalent to  


x%5E2+%2B+4x+%2B+k%2F2 = 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%2F2 is the product of the roots  (-3)*(-1) = 3  (the Vieta's theorem).  Hence, k = 2*3 = 6.

Solved.

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To see more solved problems on Vieta's theorem, look into the lesson
    - Using Vieta's theorem to solve qudratic equations and related problems
in this site.