document.write( "Question 1087254: Two numbers differs by 7. The product is less than 78.find possible range of values of smaller number \n" ); document.write( "

Algebra.Com's Answer #701524 by htmentor(1343) $\"\"$ $\"About$

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Let x = the smaller number
\n" ); document.write( "Then the larger number is x+7
\n" ); document.write( "Their product is less than 78:
\n" ); document.write( "x(x+7) < 78
\n" ); document.write( "x^2 + 7x - 78 < 0
\n" ); document.write( "In other words, we need to find the intervals where the quadratic x^2 - 7x - 78 is less than zero.
\n" ); document.write( "The quadratic can be factored as (x-6)(x+13), so the zeros are x=6 and x=-13
\n" ); document.write( "Since the leading term is positive, the parabola opens up and crosses zero at x=6 and x=-13.
\n" ); document.write( "So the range of values are -13 < x < 6 \n" ); document.write( "

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