document.write( "Question 1144405: Find all values of h for which the quadratic equation has two real solutions. 3x^2+7x +h=0. Write your answer as an equality or inequality in terms of h. \n" ); document.write( "

Algebra.Com's Answer #765508 by ikleyn(52782) $\"\"$ $\"About$

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

\r\n" );
document.write( "\r\n" );
document.write( "A quadratic equation  ax^2 + bx + c = 0  has two distinct real roots if and only if the discriminant  b^2-4ac  is POSITIVE.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "For your example,\r\n" );
document.write( "\r\n" );
document.write( " > \r\n" );
document.write( "\r\n" );
document.write( "49-12h > 0\r\n" );
document.write( "\r\n" );
document.write( "49 > 12h\r\n" );
document.write( "\r\n" );
document.write( "h < 49/12\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Compare my solution and my answer with that of the tutor @greenestamps and notice\r
\n" ); document.write( "\n" ); document.write( "that my inequality signs are always STRICT inequalities to provide $\"highlight%28two%29\"$ real solutions, as the problem requires.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you admit merging two solutions into one, then you can use the solution by @greenestamps.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you do not admit such merging, then you should use my solution and my answer.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            Unfortunately, the exact meaning of the problem and of the question is not clear from the post.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "--------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To learn everything about quadratic equations, look into 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( "    - HOW TO complete the square - Learning by examples \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 Vieta's theorem to solve qudratic equations and related problems\r
\n" ); document.write( "\n" ); document.write( "    - Using quadratic equations to solve word problems\r
\n" ); document.write( "\n" ); document.write( "    - Challenging word problems solved using quadratic equations \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( "    - OVERVIEW of lessons on solving quadratic equations\r
\n" ); document.write( "\n" ); document.write( "in this site.\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
\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( "Quadratic equations is one of the key topics in Elementary algebra -- therefore, make all efforts to learn everything about them.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );