document.write( "Question 444397: quadratic equations, which are expressed in the form of ax^2 + bx + c=0, where a does not equal 0, may have how many solutions? explain why. \n" ); document.write( "

Algebra.Com's Answer #306340 by poliphob3.14(115) $\"\"$ $\"About$

You can put this solution on YOUR website!
To find the solutions of quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ where a≠0, we\r
\n" ); document.write( "\n" ); document.write( "divide both sides by a: $\"%28x%5E2%2B%28b%2Fa%29x+%2Bc%2Fa%29=0\"$ , complete the square:\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2B%28b%2Fa%29x%2Bb%5E2%2F4a%5E2%29=b%5E2%2F4a%5E2-c%2Fa\"$ => $\"%28x%2Bb%2F2a%29%5E2=%28b%5E2-4ac%29%2F4a%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "Based on square root definition we have: $\"x=%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F2a\"$ \r
\n" ); document.write( "\n" ); document.write( "If $\"b%5E2-4ac=0\"$ we have one solution: $\"x=-b%2F2a\"$ .\r
\n" ); document.write( "\n" ); document.write( "If $\"b%5E2-4ac\"$ ≠0 we have two different solutions:\r
\n" ); document.write( "\n" ); document.write( " $\"x%5B1%5D=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F2a\"$ and $\"x%5B2%5D=%28-b-sqrt%28b%5E2-4ac%29%29%2F2a\"$ \r
\n" ); document.write( "\n" ); document.write( "If $\"b%5E2-4ac%3C0\"$ the equation has no real solutions. \n" ); document.write( "

\n" );