The polynomial `x^4 + 3x^3 + ax + 3` is denoted by p(x). It is given that p(x) is divisible by `x^2-x + 1` . Find the real roots of the equation p(x) = 0

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Since the polynomial is divisible by `x^2-x+1` we can say;

`x^4+3x^3+ax+3 = (x^2-x+1)(px^2+qx+r)`

`x^4+3x^3+ax+3 = px^4+qx^3+rx^2-px^3-qx^2-rx+px^2+qx+r`

`x^4+3x^3+ax+3 = px^4+(q-p)x^3+(r-q+p)x^2+(q-r)+r`


(The entire section contains 130 words.)

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