Question

Find the values of m and n so that x×4 + mx×3 + nx×2 -3x + n is divisible by x×2 - 1

Answer 1

x⁴ + mx³ + nx² - 3x + n is divisible by x² - 1
Or you can say that (x² - 1) = 0 , x = ± 1 are the zeros of x⁴ + mx³ + nx² - 3x + n
Then, put x = 1
(1)⁴ + m(1)³ + n(1)² - 3(1) + n = 0
⇒ 1 + m + n - 3 + n = 0
⇒ m + 2n - 2 = 0
⇒ m + 2n = 2 --------(1)

Put x = -1
(-1)⁴ + m(-1)³ + n(-1)² - 3(-1) + n = 0
⇒1 - m + n + 3 + n = 0
⇒- m + 2n + 4 = 0
⇒- m + 2n = - 4 ---------(2)

from equations (1) and (2)
4n = -2 , n = -1/2 and m = -3

Answer 2

here is the answer

hope it helps you