document.write( "Question 1144125: Can someone help me with this? Thank you.
\n" ); document.write( "I need to find all the zeros of the function f(x)=-2x^4-5x^3-5x^2-20x+12, given -3 is a zero.
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Algebra.Com's Answer #765126 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "You can apply the \"Rational roots theorem\" first.\r\n" );
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document.write( "The theorem will tell you that possible rational roots are among some finite set of rational and integer numbers. \r\n" );
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document.write( "It is good, but does not help too much.\r\n" );
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document.write( "Therefore, in such cases I simply make a plot of the polynomial, and the plot (see the Figure below) points you \r\n" );
document.write( "all possible real / rational / integer roots.\r\n" );
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document.write( "    Plot y = \r\n" );
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document.write( "In this case the roots -3 and  are pointed.\r\n" );
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document.write( "Surely, having this tip, you should check directly that these numbers really are the roots.\r\n" );
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document.write( "But if it is so, then the polynomial is divisible by the binomials  (x-(-3)) = (x+3)  and  (2x-1).\r\n" );
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document.write( "Thus the polynomial should be divisible by the product  (x+3)*(2x-1) = 2x^2 + 5x - 6 without a remainder.\r\n" );
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document.write( "So, make this long division and find the quotient. The quotient will be the polynomial of the degree 2 (quadratic).\r\n" );
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document.write( "Finding the roots of this quadratic is elementary job. (The rest of the roots could be complex numbers, though).\r\n" );
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document.write( "In this way, you will get the answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Notice that I communicate with you, assuming that you are a real student, who knows some basics (adequate to the problem)
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