document.write( "Question 62015: P(x)=x^3-5x+2 it ask me to find all the real zeros of the polynomial \n" ); document.write( "

Algebra.Com's Answer #42781 by Nate(3500) $\"\"$ $\"About$

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Descarte's Rule of Signs:
\n" ); document.write( "P(x) = (+) x^3 (+-) 0x^2 (-) 5x^1 (+) 2x^0
\n" ); document.write( "P(-x) = (-) x^3 (+-) 0x^2 (+) 5x^1 (+) 2x^0
\n" ); document.write( "Pos: 2 .. 0
\n" ); document.write( "Neg: 1 .. 1
\n" ); document.write( "Img: 0 .. 2
\n" ); document.write( "We now know that there is definetly a negative zero.
\n" ); document.write( "P(x) = x^3 - 5x + 2
\n" ); document.write( "a = 1,2
\n" ); document.write( "b = 1
\n" ); document.write( "+- a/b = +- 1 and +- 2
\n" ); document.write( "Synthetic Division:
\n" ); document.write( "2.|......1......0......-5......2......
\n" ); document.write( "............1......2......-1.......0
\n" ); document.write( "(x - 2)(x^2 + 2x - 1) = P(x)
\n" ); document.write( "x^2 + 2x - 1 = 0
\n" ); document.write( "x^2 + 2x = 1
\n" ); document.write( "(x + 1)^2 = 2
\n" ); document.write( "x + 1 = +- sqrt(2)
\n" ); document.write( "x = -1 +- sqrt(2)
\n" ); document.write( "Zeros:
\n" ); document.write( "x = 2
\n" ); document.write( "x = -1 + sqrt(2)
\n" ); document.write( "x = -1 - sqrt(2)
\n" ); document.write( " $\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E3+-+5x+%2B+2%29\"$ \n" ); document.write( "

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