The GATE Grind

GATE 2022 CS – Question 3

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

Let $r$ be a root of the equation $x^2+2x+6=0$. Then the value of the expression $(r+2)(r+3)(r+4)(r+5)$ is

  1. 51
  2. $-51$
  3. 126
  4. $-126$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (D) $-126$

Explanation

Pair the factors: $(r+2)(r+5)=r^2+7r+10=5r+4$ and $(r+3)(r+4)=r^2+7r+12=5r+6$, using $r^2=-2r-6$. Their product is $25r^2+50r+24=25(-2r-6)+50r+24=-126$.