If x , y and z are the roots of the equation 2 t 3 - tan ⁡ x + y + z π t 2 - 111 t + 2020 = 0 , then x y z y z x z x y is equal to (where, x denotes the greatest integral value less than or equal to x )

Question

If x , y and z are the roots of the equation 2 t 3 - tan ⁡ x + y + z π t 2 - 111 t + 2020 = 0 , then x y z y z x z x y is equal to (where, x denotes the greatest integral value less than or equal to x ), 20, – 10, 0, 1

MARKS App · Accepted Answer

x + y + z is an integer ⇒ tan ⁡ x + y + z π = 0 Hence, the sum of roots = x + y + z = 0 ⇒ x y z y z x z x y = - x + y + z x 2 + y 2 + z 2 - x y - y z - z x = 0

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