KVPY 2019 SB SX Exam Previous Papers

Question : 5 of 120

Marks: +1, -0

The number of integers x satisfying

–3x^4 + \det|\table 1,x,x^2 ;1,x^2,x^4;1,x^3,x^6|= 0

is equal to

Solution:

|\table 1,x,x^2 ;1,x^2,x^4;1,x^3,x^6|=3x^4

⇒

(x -x ^2 ) (x^2 -x ^3 ) (x^3 -x) = 3x^4

⇒

x = 0 \or\ (1-x)^2(x^2 -1) = 3

⇒

x^4 -2x^3 + 2x -4 = 0

⇒

(x -2) (x^3 + 2) = 0

⇒ integer values are 0, 2

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