If α and β are the roots of x2-a(x-1)+b=0, then the value of 1/[ɑ2-aɑ]+1/[β2-aβ]+2/[a+b] is
4/(a+b)
1/(a+b)
0
-1
Explanation for correct option:
Find the value of 1/[ɑ2-aɑ]+1/[β2-aβ]+2/[a+b]:
Since α and β are the roots of x2-a(x-1)+b=0
⇒β2–a(β–1)+b=0⇒β2–aβ=–(a+b)
and α2-a(α-1)+b=0
⇒α2-aα=-(a+b)
Thus
1ɑ2-aɑ+1β2-aβ+2a+b=-1a+b-1a+b+2a+b=0
Hence, the correct option is C.
If α and β are the roots of the equation x2−a(x+1)−b=0, then (α+1)(β+1)=