document.write( "Question 549316: Find all zeros of h(x)= x³ - 9x² + 19x - 35. \n" ); document.write( "
Algebra.Com's Answer #357708 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Find all zeros of h(x)= x³ - 9x² + 19x - 35
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document.write( "If there are any rational zeros they have to be ± a divisors of 35.\r\n" );
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document.write( "So we try 5\r\n" );
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document.write( "5|1 -9  19 -35\r\n" );
document.write( " |   5 -20  -5\r\n" );
document.write( "  1 -4  -1 -40 \r\n" );
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document.write( "Nope, 5 is not a zero.\r\n" );
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document.write( "So try 7\r\n" );
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document.write( "7|1 -9  19 -35\r\n" );
document.write( " |   7 -14  35\r\n" );
document.write( "  1 -2   5   0\r\n" );
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document.write( "Yep that's a zero, so we have now factored h(x) as\r\n" );
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document.write( "h(x)= x³ - 9x² + 19x - 35\r\n" );
document.write( "h(x)= (x - 7)(x² - 2x + 5)\r\n" );
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document.write( "Set each factor = 0\r\n" );
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document.write( "x - 7 = 0     x² - 2x + 5 = 0\r\n" );
document.write( "    x = 7\r\n" );
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document.write( "The first gives back the factor we just found.\r\n" );
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document.write( "The second must be solved with the quadratic formula:\r\n" );
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document.write( "x = \"%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"\r\n" );
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document.write( "x = \"%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A%281%29%2A%285%29+%29%29%2F%282%2A%281%29%29+\"\r\n" );
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document.write( "x = \"%282+%2B-+sqrt%284-20+%29%29%2F2+\"\r\n" );
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document.write( "x = \"%282+%2B-+sqrt%28-16+%29%29%2F2+\"\r\n" );
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document.write( "x = \"%282+%2B-+i%2Asqrt%2816+%29%29%2F2+\"\r\n" );
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document.write( "x = \"%282+%2B-+4i%29%2F2+\"\r\n" );
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document.write( "x = \"%282%281+%2B-+2i%29%29%2F2+\"\r\n" );
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document.write( "x = \"%28cross%282%29%281+%2B-+2i%29%29%2Fcross%282%29+\"\r\n" );
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document.write( "x = 1 ± 2i\r\n" );
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document.write( "The 3 zeros are 7, 1 + 2i, and 1 - 2i \r\n" );
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document.write( "Find all zeros of \r\n" );
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document.write( "f(x)= x³ - 2x² + 25x - 50\r\n" );
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document.write( "That one can be factored by grouping:\r\n" );
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document.write( "Factor x² out of the first two terms and 25 out of the last two:\r\n" );
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document.write( "f(x) = x²(x - 2) + 25(x - 2)\r\n" );
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document.write( "Factor (x - 2) out of both terms:\r\n" );
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document.write( "f(x) = (x - 2)(x² + 25)\r\n" );
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document.write( "Set each = 0:\r\n" );
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document.write( "x - 2 = 0\r\n" );
document.write( "    x = 2\r\n" );
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document.write( "x² + 25 = 0\r\n" );
document.write( "     x² = -25\r\n" );
document.write( "      x = \"%22%22+%2B-+sqrt%28-25%29\"\r\n" );
document.write( "      x = \"%22%22+%2B-+i%2Asqrt%2825%29\"\r\n" );
document.write( "      x = ±5i\r\n" );
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document.write( "The three zeros are 2, 6i, and -5i\r\n" );
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document.write( "Edwin

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