document.write( "Question 916646: The function p is a fourth-degree polynomial with x-intercepts 1, 4, and 10 and y-intercept -2. If p(x) is positive only on the interval (4, 10), find p(x). \n" ); document.write( "

Algebra.Com's Answer #556217 by josgarithmetic(39617) $\"\"$ $\"About$

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The description means that p crosses the x-axis at 4 and 10; but p only touches (does not cross) the x-axis at 1. THIS is the root which has multiplicity of 2. \r
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\n" ); document.write( "\n" ); document.write( " $\"p%28x%29=a%28x-1%29%5E2%28x-4%29%28x-10%29\"$ \r
\n" ); document.write( "\n" ); document.write( "You should find that $\"a%3C0\"$ , and get its value using $\"p%280%29=-2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "(approximately, $\"a=-%281%2F20%29\"$ , but let x=0 and solve for a to be sure.)\r
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