document.write( "Question 16789: I'm problems with the following problem in understanding it.
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\n" ); document.write( "Find a polynomial with leading coefficient 1 and degree 3 that has -1, 1, and 3 as roots.
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\n" ); document.write( "It seems pretty easy and I think the answer is x^3-3x^2-x-3, but that just from looking at it. I'm not sure how to actually do the problem.
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\n" ); document.write( "Thanks for any help \n" ); document.write( "

Algebra.Com's Answer #8212 by xcentaur(357)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Now let the polynomial be \r\n" );
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document.write( "x^3-ax^2+bx-c=0\r\n" );
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document.write( "Let the roots be p,q,and r.\r\n" );
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document.write( "Then a=p+q+r\r\n" );
document.write( "     b=pq+qr+pr\r\n" );
document.write( "     c=pqr\r\n" );
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document.write( "since the roots are given as -1,1 and 3,we get\r\n" );
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document.write( "a=-1+1+3=3\r\n" );
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document.write( "b=(-1*1)+(1*3)+(-1*3)=-1\r\n" );
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document.write( "c=(-1)(1)(3)=-3\r\n" );
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document.write( "substituting,\r\n" );
document.write( "x^3-ax^2+bx-c=0\r\n" );
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document.write( "x^3-(3)x^2+(-1)x-(-3)=0\r\n" );
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document.write( "x^3-3x^2-x+3=0\r\n" );
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document.write( "Now this can be verified for a polynomial as:\r\n" );
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document.write( "(x-p)(x-q)(x-r)=f(x)\r\n" );
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document.write( "(x-(-1))(x-(+1))(x-(+3))\r\n" );
document.write( "(x-1)(x+1)(x-3)\r\n" );
document.write( "On expanding we get the expression that we just worked out. Thus we know that our polynomial is indeed correct.\r\n" );
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\n" ); document.write( "Hope this helps,
\n" ); document.write( "Prabhat \n" ); document.write( "

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