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.
———————————————————————————————

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^4 - x^3 + 11x^2 -7x +28 = highlight( (x^2+7)(x^2-x+4)  ) }}}

{{{ (x^2+7) = 0 }}} has only imaginary roots, so  only {{{ (x^2-x+4)= 0 }}}  has to be considered

    {{{ x = (1 +- sqrt(1 - 4*1*4) )/(2*1) = (1 +- sqrt(-15) )/2 }}}  —> imaginary/complex roots.

No real values of p were found.