SOLUTION: Find real values of p for which pi is a root of x^4 - x^3 + 11x^2 -7x +28=0. Hence,write the equation as a product of two quadratic factors.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find real values of p for which pi is a root of x^4 - x^3 + 11x^2 -7x +28=0. Hence,write the equation as a product of two quadratic factors.      Log On


   

Question 1081856: Find real values of p for which pi is a root of x^4 - x^3 + 11x^2 -7x +28=0.
Hence,write the equation as a product of two quadratic factors.
Answer by math_helper(2461) About Me  (Show Source):
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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.
Hence,write the equation as a product of two quadratic factors.
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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).

From Wolfram Alpha: +x%5E4+-+x%5E3+%2B+11x%5E2+-7x+%2B28+=+highlight%28+%28x%5E2%2B7%29%28x%5E2-x%2B4%29++%29+
+%28x%5E2%2B7%29+=+0+ has only imaginary roots, so only +%28x%5E2-x%2B4%29=+0+ has to be considered
+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.
No real values of p were found.