document.write( "Question 1161407: my question is Create an example of a quadratic equation that can be factored and solved with non-integer solutions. what would i use? and how would i apply to make this question?
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Algebra.Com's Answer #784942 by KMST(5328) $\"\"$ $\"About$

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A quadratic equation that can be factored will end up factored into the from $\"K%28x-a%29%28x-b%29=0\"$ , where $\"a\"$ and $\"b\"$ are the solutions, and K is the coefficient of the term with $\"x%5E2\"$ , with an integer nonzero value for $\"K\"$
\n" ); document.write( "In practice, factoring works best when $\"K=1\"$ while $\"a\"$ and $\"b\"$ are integers.
\n" ); document.write( "However, you can factor quadratic equations that have rational solutions that are not integers.
\n" ); document.write( "It would be easy to make one.
\n" ); document.write( "Let us make $\"a=1%2F2\"$ and $\"b=2%2F3\"$ .
\n" ); document.write( " $\"%28x-a%29%28x-b%29=%28x-1%2F2%29%28x-1%2F3%29=x%5E2-%285%2F6%29x%2B1%2F6\"$
\n" ); document.write( " $\"x%5E2-5%2F6%2B1%2F6=0\"$ has non-integer solutions,
\n" ); document.write( "but students may not find it too easy to factor.
\n" ); document.write( "We like integer coefficients, anyway,
\n" ); document.write( "so we multiply both sides of the equal sign times $\"6\"$ to get
\n" ); document.write( " $\"6x%5E2-5x%2B1=0\"$ .
\n" ); document.write( "You can take any two rational numbers and do the same trick.
\n" ); document.write( "That is probably what is expected for the quadratic equation \"creation.\"
\n" ); document.write( "You could also start from any product of binomials with integer coefficients where the coefficients of x are not 1.
\n" ); document.write( " $\"%282x%2B7%29%283x-1%29=0\"$ is equivalent to $\"6x%5E2%2B19x-7=0\"$ and would work.
\n" ); document.write( "You can see that the solutions are $\"x=-7%2F2\"$ and $\"x=1%2F3\"$ .
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\n" ); document.write( "There is also the case that if the two solutions are opposites, $\"a\"$ and $\"-a\"$ , the equation is $\"%28x%2Ba%29%28x-a%29=0\"$ or $\"x%5E2+-a%5E2=0\"$ .
\n" ); document.write( "Fr $\"a=1%2F3\"$ we would get $\"x%5E2-1%2F9=0\"$ ,
\n" ); document.write( "and present it as the equivalent form
\n" ); document.write( " $\"9x%5E2-1=0\"$ , which can be factored as can be factored as
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\n" ); document.write( "To be a smartalec, I could argue that I can factor $\"x%5E2+-pi=0\"$ into
\n" ); document.write( " $\"%28x-sqrt%28pi%29%29%28x%2Bsqrt%28pi%29%29=0\"$ , to find the non-integer solutions
\n" ); document.write( " $\"sqrt%28pi%29\"$ and $\"-sqrt%28pi%29\"$ , but only if the teacher had a sense of humor. \n" ); document.write( "

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