document.write( "Question 1110465: For the quadratic equation, find the value of the discriminant and give the number of real solutions.
\n" ); document.write( "3x^2+8x=0 \n" ); document.write( "

Algebra.Com's Answer #725437 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "Referring to the general form of a quadratic polynomial/equation\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    p(x) = ax^2 + bx + c = 0 \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "the formula for the discriminant is \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    d = b^2 - 4ac.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In your case,  a = 3, b = 8, c = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Calculate the discriminant on your own.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "If d > 0, there are 2 real solution.\r\n" );
document.write( "\r\n" );
document.write( "If d = 0, there is only one real solution  (\"two real solutions merge into one\").\r\n" );
document.write( "\r\n" );
document.write( "If d < 0,  there are no real solution. (There are two complex solutions instead).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Having this instructions from me, you do the rest.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "--------------------
\n" ); document.write( "On solving quadratic equations see the lessons \r
\n" ); document.write( "\n" ); document.write( "    - Introduction into Quadratic Equations\r
\n" ); document.write( "\n" ); document.write( "    - PROOF of quadratic formula by completing the square\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "My other lessons on solving quadratic equations in this site are \r
\n" ); document.write( "\n" ); document.write( "    - HOW TO solve quadratic equation by completing the square - Learning by examples \r
\n" ); document.write( "\n" ); document.write( "    - Solving quadratic equations without quadratic formula\r
\n" ); document.write( "\n" ); document.write( "    - Who is who in quadratic equations\r
\n" ); document.write( "\n" ); document.write( "    - Using quadratic equations to solve word problems\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO solve the problem on quadratic equation mentally and avoid boring calculations \r
\n" ); document.write( "\n" ); document.write( "    - Using Vieta's theorem to solve qudratic equations and related problems\r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on solving quadratic equations\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the topic \"Quadratic equations\". \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );