document.write( "Question 1030147: The polynomial f(x) has degree 3. If f(-1) = 15, f(0)= 0, $f(1) = -5, and f(2) = 12, then what are the $x$-intercepts of the graph of f?
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Algebra.Com's Answer #645124 by robertb(5830)\"\" \"About 
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Let \"f%28x%29+=+ax%5E3+%2B+bx%5E2+%2Bcx+%2B+d\".
\n" ); document.write( "Since f(0)= 0, ==> d = 0\r
\n" ); document.write( "\n" ); document.write( "==> \"f%28x%29+=+ax%5E3+%2B+bx%5E2+%2Bcx\"
\n" ); document.write( "Now f(-1) = 15 ==> -a + b - c = 15, while
\n" ); document.write( "f(1) = -5 ==> a + b + c = -5.
\n" ); document.write( "Adding the corresponding sides of the two preceding equations, we get b = 5.
\n" ); document.write( "==> a + c = -10 <--------Equation (A)\r
\n" ); document.write( "\n" ); document.write( "f(2) = 12 ==> 8a + 4b + 2c = 12 ==> 8a+20+2c = 12, or \r
\n" ); document.write( "\n" ); document.write( "4a+c = -4 <----------Equation (B)\r
\n" ); document.write( "\n" ); document.write( "after simplifying...
\n" ); document.write( "Solving for a and c from Equations A and B, we get a = 2 and c = -12.\r
\n" ); document.write( "\n" ); document.write( "==> \"f%28x%29+=+2x%5E3+%2B+5x%5E2+-+12x+=+x%282x-3%29%28x%2B4%29\".\r
\n" ); document.write( "\n" ); document.write( "The roots correspond to the x-coordinates of the x-intercepts. Thus the x-intercepts are (0,0), (3/2,0), and (-4,0).
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