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Answer to Question #27992 in Differential Equations for Luke

Question #27992
The roots of the equation 4x-squared + kx = 9, differ by 5. Calculate the value(s) of k
Expert's answer
4x^2+kx-9=0. Let's divide both parts of the equation by 4.
x^2+(k/4)x-9/4=0
Let A be one of the roots, then the other is A+5. Using Vieta's formulas, we have:
(1) A+A+5=-k/4;
(2) A*(A+5)=-9/4.
Now we solve the (2) equation. A1=-1/2,A2=-9/2. So there are to value of k.
If A=-1/2, then k=-16. (form (1) equation)
If A=9/2, then k=16.

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