Let α, β be the roots of the equation (x – a) (x – b) = c, c ≠

1.	Let α, β be the roots of the equation (x – a) (x – b) = c, c ≠ 0, then the roots of the equation (x – α) (x – β) + c = 0 are :(a) a, c (b) b, c (c) a, b (d) a + c, b + c
Answer» (c) a, b The given equation is (x – a) (x – b) = c ⇒ x² – (a + b)x + (ab – c) = 0 As α, β are the roots of this equation, so α + β = a + b and αβ = ab – c Let γ , δ be the roots of the equation (x – α) (x – β) + c = 0 i.e., γ , δ are the roots of the equation x² – (α + β)x + (αβ + c)= 0 ∴ γ + δ = α + β = a + b ...(i) γδ = αβ + c = – c + c = ab ...(ii) ∴ From (i) and (ii) we can infer that the roots of the equation (x – α) (x – β) + c = 0 are a and b.

Let α, β be the roots of the equation (x – a) (x – b) = c, c ≠ 0, then the roots of the equation (x – α) (x – β) + c = 0 are :(a) a, c (b) b, c (c) a, b (d) a + c, b + c

Answer»

(c) a, b

The given equation is (x – a) (x – b) = c

⇒ x² – (a + b)x + (ab – c) = 0

As α, β are the roots of this equation, so

α + β = a + b and αβ = ab – c

Let γ , δ be the roots of the equation (x – α) (x – β) + c = 0

i.e., γ , δ are the roots of the equation x² – (α + β)x + (αβ + c)= 0

∴ γ + δ = α + β = a + b ...(i)

γδ = αβ + c = – c + c = ab ...(ii)

∴ From (i) and (ii) we can infer that the roots of the equation

(x – α) (x – β) + c = 0 are a and b.