Question

If α and β are the roots of the equation x2 - q(1+x) - r = 0, then what is (1+α)(1+β) equal to?

1 - r
q - r
1 + r
q + r

Answer 1

Answer:

x2 - q - qx - r = 0

x2 - qx - (q + r) = 0

Sum of roots = α + β = -b/a = q

Product of roots = αβ = c/a = -(q+r)

(1+α)(1+β) = 1 + (α+β) + αβ

= 1 + q - q - r  

= 1 - r

The correct option is A.