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GATE 2022 BM – Question 3

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

If r is a root of x²+2x+6=0, find (r+2)(r+3)(r+4)(r+5).

  1. 51
  2. −51
  3. 126
  4. −126

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Correct answer: (D) −126

Explanation

Use r²=−2r−6. Pairing factors gives (r+2)(r+4)=4r+2 and (r+3)(r+5)=6r+9. Their product is 24r²+48r+18=24(−2r−6)+48r+18=−126. This holds for either complex root. Choose D.

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