Question

find the values of m and n if the polynomial 2x^3+mx^2+nx-14 has x-1and x+2 as its factors

Answer 1

Sol'n: For zero,

x - 1 = 0
=> x = 1

and x + 2 = 0
=> x = -2

Therefore, p(1) = 0
=> 2 × 1³ + m × 1² + n × 1 - 14 = 0
=> 2 + m + n - 14 = 0
=> m + n = 12 ————> (i)

and p(-2) = 0
=> 2 × (-2)³ + m × (-2)² + n × (-2) - 14 = 0
=> -16 + 4m - 2n - 14 = 0
=> 4m - 2n = 30 ————> (ii)

Now,

equ'n (i) × 4
=> 4m + 4n = 48
4m + 2n = 30
(-) (-) (-)
-------------------------------
2n = 18
=> n = 18/2
=> n = 9

Putting n = 9 in equ'n (i), we get

m + n = 12
=> m + 9 = 12
=> m = 12 - 9
=> m = 3

Therefore, m = 3 and n = 9

HOPE IT'LL HELP...:)