Theory of Equations 3 Question 1

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(1992,2M)

Show Answer

Answer:

Correct Answer: 1. (c)

Solution:

  1. Given, α,β are the roots of (x−a)(x−b)−c=0

⇒(x−a)(x−b)−c=(x−α)(x−β)

⇒(x−a)(x−b)=(x−α)(x−β)+c

⇒a,b are the roots of equation (x−α)(x−β)+c=0

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