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Question 1094823: The equation x^2+(k+2)x+2k=0 has two distinct real roots.
Find the possible values of k.
Answer by ikleyn(52747)   (Show Source):
You can put this solution on YOUR website! .
HINT: the discriminant must be positive.
Refering to general quadratic equation form ax^2 + bx + c = 0, the discriminant is d = b^2-4ac.
In your case b = (k+2), c = 2k, a = 1.
So, the discriminant is d = b^2 - 4ac = (k+2)^2 - 4*1*2k = k^2 + 4k + 4 - 8k = k^2 - 4k + 4 = (k-2)^2.
The requirement d > 0 means that k =/= 2.
It is your answer: k =/= 2.
Solved.
Notice that if k = 2, then the two real roots merge to one.
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On discriminant and the roots of a quadratic equation see the lessons
- Introduction into Quadratic Equations
- PROOF of quadratic formula by completing the square
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this textbook under the topic "Quadratic equations".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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