A point and an equation

Algebra Level 3

there is a point on the cartesian plane, which, when joined to the origin, makes an angle of \(45^\circ\) with the x axis.

the coordinates of this point is \((a,b)\), and \(a\) and \(b\) are the zeroes of the equation \(cx^2+dx+e=0\) and \(ex^2+dx+c=0\).

it is provided that \(d<0\) and \(c>0\).

find c+d+e+1.


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