GATE | CS 2022 | Question 3

Let r be a root of the equation x² + 2x + 6 = 0. Then the value of the expression (r+2) (r+3)(r+4)(r+5) is 

(A)

51

(B)

 -51

(C)

126

(D)

-126

Answer:(D)
Explanation:

r is a root of the quadratic equation x²+2x+6=0

x² + 2x +6 =0

So, r² + 2r +6 =0

     = (r+2)(r+3)(r+4)(r+5)

     = 

      = 3r(7r + 14)

       = 

       =-126

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