Look at the constant term

Algebra Level 5

If the roots of the polynomial equation \[\large {4x^{4}+6x^{3}+2x^{2}+2003x-4012009\,=\,0}\] are of the form \[ \dfrac{-a \pm \sqrt{b}}{c} \,\,\,\, , \,\,\,\, \dfrac{-a \pm i \cdot 7 \sqrt{(a+c) \cdot d}}{c^{2}}\], where \(b\), \(c\) and \(d\) are primes. Find \(\color{blue}{a+b+c+d}\).

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