document.write( "Question 61245: Please, Please, PLEASE I REALLY need help on these 2 problems.\r
\n" ); document.write( "\n" ); document.write( "f(x)=2x^3+7x^2+x+3, use the rational zeros theorem to find and list all the possible values of p/q.\r
\n" ); document.write( "\n" ); document.write( "Given the equation P(x)=2x^3+7x^2+x+3 how many variations of sign are there, in the sense of Descartes' rule of signs? What is the number of positive real zeros of P(x)?
\n" ); document.write( " If anyone has the time and feels like helping, thanks in advance. \n" ); document.write( "
Algebra.Com's Answer #42205 by funmath(2933)\"\" \"About 
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In the equation P(x) = 2x^3 + 7x^2 + x + 3 how many variations of sign are there, in the sense of Descartes’ rule of signs? What is the number of positive real zeros of P(x)?
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\n" ); document.write( "First note that a polynomial cannot have more real zeroes than its degree. The most zeros this polynomial can have is 3, because this is a third degree polynomial.
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\n" ); document.write( "The Descartes' Rule of Signs States:
\n" ); document.write( "Let f denote a polynomial function written in standard form.
\n" ); document.write( "*The number of positive real zeroes of f either equals the number of variations in the sign of the nonzero coefficients of f(x) or else equals that number less an even integer.
\n" ); document.write( "*The number of negative real zeroes of f either equlas the number of variations in the sign of f(-x) or else equals that number less an even integer.
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\n" ); document.write( "P(x) is always positive (++)(++)(++), the terms never change from + to - or - to +, therefore there are no positive zeros.
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\n" ); document.write( "P(-x)=2(-x)^3+7(-x)^2+(-x)+3
\n" ); document.write( "P(-x)=-2x^3+7x^2-x+3
\n" ); document.write( "Has 3 variations of signs (-+),(+-),(-+), that means you can have 3 (or 3-2=1) negative zeroes.
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\n" ); document.write( "Happy Calculating!!!
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