document.write( "Question 707166: Without solving, find the product and the sum of the roots for 4x^2-7x+3\r
\n" ); document.write( "\n" ); document.write( "I know that a=4 b=-7 & c=3, I also have the equation, x^2+(-7)/4x +3/4 but I have no idea where to go from there, So where do I go from there?
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Algebra.Com's Answer #435547 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
You have the right values for a, b and c and that is all you need. You do not need to change the expression.

\n" ); document.write( "The sum of the roots of a quadratic is -b/a. So the sum of the roots for your expression will be -(-7)/(4) which simplifies to: 7/4

\n" ); document.write( "The product of the roots of a quadratic will be c/a. So the product of the roots to your expression will be (3)/(4) = 3/4

\n" ); document.write( "If you didn't know that the sum was -b/2a and/or that the product was c/a then it is not terribly difficult to figure this out on your own. From the Quadratic Formula we know that the roots of a general quadratic equation will be:
\n" ); document.write( "\"x%5B1%5D+=+%28-b+%2B+sqrt%28b%5E2-4ac%29%29%2F2a\" and \"x%5B2%5D+=+%28-b+-+sqrt%28b%5E2-4ac%29%29%2F2a\"
\n" ); document.write( "Splitting these into two separate fractions will help with the rest:
\n" ); document.write( "\"x%5B1%5D+=+%28-b%29%2F2a+%2B+sqrt%28b%5E2-4ac%29%29%2F2a\" and \"x%5B2%5D+=+%28-b%29%2F2a+-+sqrt%28b%5E2-4ac%29%2F2a\"

\n" ); document.write( "Now let's see what the sum looks like. If you look at \"x%5B1%5D\" and \"x%5B2%5D\" it should be easy to see that the second fractions will cancel each other out because one is positive and the other is negative. So when we add will will get:
\n" ); document.write( "\"%28-b%29%2F2a+%2B+%28%28-b%29%2F2a%29+=+%28-2b%29%2F2a+=+%28-b%29%2Fa\"

\n" ); document.write( "Now let's see what the product looks like:
\n" ); document.write( ". If we look at this we should be able to see that this fits the \"p%2Bq%29%28p-q%29\" pattern. And from the pattern we know that the result is \"p%5E2-q%5E2\". Using this pattern will save us time in multiplying:
\n" ); document.write( "\"%28%28-b%29%2F2a%29%5E2+-+%28sqrt%28b%5E2-4ac%29%29%2F2a%29%5E2%29\"
\n" ); document.write( "which simplifies as follows:
\n" ); document.write( "\"b%5E2%2F4a%5E2+-+%28b%5E2-4ac%29%2F4a%5E2%29\"
\n" ); document.write( "These have the same denominator so we can subtract them:
\n" ); document.write( "\"%28%28b%5E2%29+-+%28b%5E2-4ac%29%29%2F4a%5E2%29\"
\n" ); document.write( "Simplifying...
\n" ); document.write( "\"4ac%2F4a%5E2%29\"
\n" ); document.write( "\"c%2Fa\"
\n" ); document.write( "(Note: I have a terrible memory. I can never remember these sum and product formulas. I always go through the above to figure them out when I need them (like now)). \n" ); document.write( "
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