A point and an equation

here it is given that the line joining the point and the origin is $45^\circ$ therefore $\tan45^\circ=\dfrac{b}{a}$ .

hence, $a=b$ .

as both the equations have same zeroes.

that is why, $ca^2+da+e=ea^2+da+c$

from this equation we get $c=e$ ,

as the equation has equal zeroes, $d^2-4c\cdot e=0$

hence, $d^2-4c^2=0$ -----------(as $c=e$ )

from the above equation we get $d=\pm2$ --------(as $d<0$ and $c>0$ )

$d=-2c$ , therefore, $c+d+e=2c-2c=0$ --------(as $c=e$ and $d=-2c$ )

hence, $c+d+e+1=\fbox{1}$