document.write( "Question 1156458: The function below has at least one rational zero. Use this fact to find all zeros of the function. Write exact values, not decimal approximations.
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\n" ); document.write( "𝑓(𝑥) = 5𝑥^4 + 32𝑥^3 − 24𝑥^2 − 20𝑥 + 7 \n" ); document.write( "
Algebra.Com's Answer #779149 by Edwin McCravy(20065)\"\" \"About 
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document.write( "𝑓(𝑥) = 5𝑥4 + 32𝑥3 − 24𝑥2 − 20𝑥 + 7\r\n" );
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document.write( "Try 𝑥 = 1\r\n" );
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document.write( "1 | 5  32  -24  -20  7\r\n" );
document.write( "  |     5   37   13 -7 \r\n" );
document.write( "    5  37   13   -7  0\r\n" );
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document.write( "Hurray, the synthetic division has a 0 on the end of the bottom\r\n" );
document.write( "row, and that tells us that 𝑥 = 1 is a zero of 𝑓(𝑥) and the other\r\n" );
document.write( "numbers across the bottom of the synthetic division tells us that \r\n" );
document.write( "we have factored 𝑓(𝑥) as\r\n" );
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document.write( "𝑓(𝑥) = (𝑥 - 1)(5𝑥3 + 37𝑥2 - 13𝑥 - 7)\r\n" );
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document.write( "We think that what's in the second parentheses might be factorable,\r\n" );
document.write( "too, so we try 𝑥 = -7 on it:\r\n" );
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document.write( "-7 | 5  37  13  -7\r\n" );
document.write( "   |   -35 -14   7\r\n" );
document.write( "     5   2  -1   0\r\n" );
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document.write( "Hurray, as before, the synthetic division has a 0 on the end of the \r\n" );
document.write( "bottom row, and that tells us that 𝑥 = -7 is a zero of both\r\n" );
document.write( "5𝑥3 + 37𝑥2 - 13𝑥 - 7 as well as 𝑓(𝑥) and the other\r\n" );
document.write( "numbers across the bottom of the synthetic division tells us that \r\n" );
document.write( "we have factored 𝑓(𝑥) further as:\r\n" );
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document.write( "𝑓(𝑥) = (𝑥 - 1)(𝑥 + 7)(5𝑥2 + 2𝑥 - 1)\r\n" );
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document.write( "What's in the last parentheses cannot be factored, so we find the\r\n" );
document.write( "zeros by setting 𝑓(𝑥) = 0 and use the zero-factor principle:\r\n" );
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document.write( "(𝑥 - 1)(𝑥 + 7)(5𝑥2 + 2𝑥 - 1)\r\n" );
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document.write( "𝑥 - 1 = 0;  𝑥 + 7 = 0,    5𝑥2 + 2𝑥 - 1 = 0\r\n" );
document.write( "    𝑥 = 1;      𝑥 = -7;  \r\n" );
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document.write( "To find the other two zeros, we must use the quadratic formula:\r\n" );
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document.write( "5𝑥2 + 2𝑥 - 1 = 0\r\n" );
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document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29+\"\r\n" );
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document.write( "\"x+=+%28-2+%2B-+sqrt%28+2%5E2-4%285%29%28-1%29+%29%29%2F%282%285%29%29+\"\r\n" );
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document.write( "\"x+=+%28-2+%2B-+sqrt%28+4%2B20+%29%29%2F%2810%29+\"\r\n" );
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document.write( "\"x+=+%28-2+%2B-+sqrt%2824+%29%29%2F10+\"\r\n" );
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document.write( "\"x+=+%28-2+%2B-+sqrt%284%2A6+%29%29%2F10+\"\r\n" );
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document.write( "\"x+=+%28-2+%2B-+2sqrt%286%29%29%2F10+\"\r\n" );
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document.write( "\"x+=+%282%28-1+%2B-+sqrt%286%29%29%29%2F10+\"\r\n" );
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document.write( "\"x+=+%28-1+%2B-+sqrt%286%29%29%2F5+\"\r\n" );
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document.write( "Edwin
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