Latest self Aptitude Question SOLUTION: F(x) is a fourth order polynomial with integer coefficients and with no common factor. The roots of F(x) are –2, –1, 1, 2. If p is a prime number greater than 97, then the la

• Placement Papers
• /
• self

self Question Papers:

(#M40020517) SELF question Keep an EYE

F(x) is a fourth order polynomial with integer coefficients and with no common factor. The roots of F(x) are –2, –1, 1, 2. If p is a prime number greater than 97, then the largest integer that divides F(p) for all values of p is

(10 years ago)

Unsolved Read Solution (1)

Is this Puzzle helpful?   (4)   (5) Submit Your Solution

Read Solution (1) :

Vidhya Anbu  (5 years ago)

Given that F(x)=(x+2)(x+1)(x−1)(x−2)
Putting x=P, we have F(P)=(P+2)(P+1)(P−1)(P−2)
Since P is a prime number, P is in form 6K±1, where K is the positive integer

F(6K+1)=(6K+3)(6K+2)(6K)(6K−1)
=(36)(2K+1)(3K+1)(K)(6K−1)——– (1)

F(6K−1)=(6K+1)(6K+2)(6K)(6K−3)
=36(6K+1)(3K+1)(K)(3K−1)——– (2)

Please note that the value of K≥17 and expression F(6K+1) and F(6K–1) always bear the factor 10.

Hence 360 is the correct choice.

Therefore option (D) is the correct choice

Is this solution Helpfull? Yes | No   

Please Login to Read Solution.