a.
If two roots are equal,then D=0
[-2 (a-1)]^2 - 4(1)[-(b+2)^2]=0
4(a-1)^2+4(b+2)^2=0
(a-1)^2+(b+2)^2=0
an^2>0 (a≠i)
a-1=0
a=1
b+2=0
b= - 2
Therefore,
a^999 + b^3
=1^999 + (-2)^3
=1-8
=-7
b.
Roots of equation are 1, -2.
For ax^2 +bx +c=0
-b/a=1+(-2)
b/a=1
a=b
c/a=1x(-2)
c/a= -2
Therefore,
One of the quadratic equation would be x^2 + bx - 2=0