document.write( "Question 1081856: Find real values of p for which pi is a root of x^4 - x^3 + 11x^2 -7x +28=0.
\n" ); document.write( "Hence,write the equation as a product of two quadratic factors. \n" ); document.write( "
Algebra.Com's Answer #695904 by math_helper(2461)\"\" \"About 
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Find real values of p for which pi is a root of x^4 - x^3 + 11x^2 -7x +28=0.
\n" ); document.write( "Hence,write the equation as a product of two quadratic factors.
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\n" ); document.write( "\n" ); document.write( "Clearly, the 'pi' \"pi\" is supposed to be 'p' (\"pi\" is transcendental which means it can not be the root of a polynomial with rational coefficients).\r
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\n" ); document.write( "From Wolfram Alpha: \"+x%5E4+-+x%5E3+%2B+11x%5E2+-7x+%2B28+=+highlight%28+%28x%5E2%2B7%29%28x%5E2-x%2B4%29++%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"+%28x%5E2%2B7%29+=+0+\" has only imaginary roots, so only \"+%28x%5E2-x%2B4%29=+0+\" has to be considered\r
\n" ); document.write( "\n" ); document.write( " \"+x+=+%281+%2B-+sqrt%281+-+4%2A1%2A4%29+%29%2F%282%2A1%29+=+%281+%2B-+sqrt%28-15%29+%29%2F2+\" —> imaginary/complex roots.\r
\n" ); document.write( "\n" ); document.write( "No real values of p were found.
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