Question 1086466
.
If the quadratic equation x2+4x+k=0 has real and {{{highlight(cross(discint))}}} distinct roots, find the value of k.
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<pre>
the quadratic equation x2+4x+k=0 has real and distinct roots  <====>  the discriminant of the equation is positive:

{{{4^2 - 4k}}} > 0  <=====>

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


<U>Answer</U>.  k < 4.
</pre>


{{{graph( 330, 330, -6.5, 3.5, -2.5, 5.5,
          x^2 + 4x + 3,  x^2 + 4x + 4, x^2 + 4x +5
)}}}


Plot y = {{{x^2 + 4x + 3}}} (red),  y = {{{x^2 + 4x + 4}}} (green), y = {{{x^2 + 4x +5}}} (blue)



On quadratic equations and their discriminants see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Introduction-Into-Quadratics.lesson>Introduction into Quadratic Equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/proof-of-quadratic-by-completing-the-square.lesson>PROOF of quadratic formula by completing the square</A>

in this site.



Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this textbook under the topic "<U>Quadratic equations</U>".