Question 1132441
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<pre>
When you have this question "Determine the Nature of the Roots", solve the problem as follows:



    - Calculate the discriminant of the equation  d = b^2 - 4ac

        (here I refer to the general form of the quadratic equation ax^2 + bx + c = 0,

         so in your case a= 1, b= 8, c -20  and  d= {{{8^2 - 4*1*(-20)}}} = 64 + 80 = 144.)



     - The discriminant is positive - so, the equation has two distinct real roots.     <U>ANSWER</U>



At this point, the question is answered and the solution is completed.



But you can make one step further to earn an additional score:


    you can easily FIND the roots  {{{x[1,2]}}} = {{{(-b +- sqrt(d))/(2a)}}} = {{{(-8 +- sqrt(144))/2}}} = {{{(-8 +- 12)/2}}} = {{{-4 +- 6}}},


    so, the roots are  {{{x[1]}}} = -4 + 6 = 2   and   {{{x[2]}}} = -4 - 6 = -10.
</pre>

Answered, solved and completed.


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On solving quadratic equations, 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>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Learning-by-examples-on-HOW-TO-complete-the-square.lesson>HOW TO complete the square - Learning by examples</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-solve-quadratic-equation-by-completing-the-square-Learning-by-examples.lesson>HOW TO solve quadratic equation by completing the square - Learning by examples</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Solving-quadratic-equations-without-quadratic-formula.lesson>Solving quadratic equations without quadratic formula</A>

in this site.


Also, &nbsp;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 &nbsp;"<U>Quadratic equations</U>". 



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.