document.write( "Question 392447: Could you help me state the degree, number of complex roots, and leading coefficient of 3x^4-x^3+5x^2+12x-7=0 \n" ); document.write( "

Algebra.Com's Answer #278570 by richard1234(7193) $\"\"$ $\"About$

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Degree is 4 since the highest power of x that has a nonzero coefficient is 4.\r
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\n" ); document.write( "\n" ); document.write( "There's a very important theorem called the Fundamental theorem of algebra (in which the proof is quite complex) that says that any single variable polynomial of degree n has n complex roots (including multiple roots). Since the degree is 4, the polynomial must have four complex roots. Note that real numbers are still considered complex, by definition.\r
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\n" ); document.write( "\n" ); document.write( "The leading coefficient is 3 (coefficient of the highest degree term). \n" ); document.write( "

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