SOLUTION: If the quadratic equation x2+4x+k=0,has real and discint roots,find the value of k.

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Question 1086466: If the quadratic equation x2+4x+k=0,has real and discint roots,find the value of k.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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x2+4x+k=0,has real and discint roots,
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"distinct" roots?

4%5E2-4%2A1%2Ak%3E0
16%3E4k
highlight%28k%3C4%29

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
If the quadratic equation x2+4x+k=0 has real and highlight%28cross%28discint%29%29 distinct roots, find the value of k.
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the quadratic equation x2+4x+k=0 has real and distinct roots  <====>  the discriminant of the equation is positive:

4%5E2+-+4k > 0  <=====>

16 - 4k > 0  <=====>  16 > 4k  <=====>  k < 4.


Answer.  k < 4.




Plot y = x%5E2+%2B+4x+%2B+3 (red), y = x%5E2+%2B+4x+%2B+4 (green), y = x%5E2+%2B+4x+%2B5 (blue)


On quadratic equations and their discriminants 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".