1.

If α, β are roots of the equation x2 -a(x+1) - c = 0, then write the value of (1+α)(1+ β).

Answer»

given x2- a(x+1) - c = 0 

x2- ax - a - c = 0 

x2- ax - (a + c) = 0 

as α, β are roots of equation, we get 

sum of the roots α + β = a 

Product of roots αβ = - (a + c) 

Given (1+ α) (1+ β) 

= 1 + (α + β) + (α β) 

= 1 + a – a – c 

= 1 – c.


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