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Question 220026
JEE Mathematics · Hard

Quadratic Equations and Inequalities: Common roots MCQ

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Common rootsHardQuestion 220026

Question

If x² + bx + c = 0 and x² + cx + b = 0 have a common root (b ≠ c), that common root is:
  1. A
    −1
  2. B
    1
    Correct
  3. C
    0
  4. D
    b + c

Correct answer

1

Explanation

Subtracting the equations gives (b−c)x+(c−b)=0(b-c)x+(c-b)=0, or (b−c)(x−1)=0(b-c)(x-1)=0. Since b≠cb≠c, the common root is x=1 (with b+c=−1b+c=-1).

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