Question

Find the values of m and n in polynomial 2x³+MX²+nx-14 such that x-1and x+2 are it's factors

Answer 1

let f (x) = 2x³ + mx² + nx - 14


Since x-1 is factor so
f (1) = 0
2(1)³ + m(1)² + n(1) - 14 = 0
2 + m + n - 14 = 0
m + n = 12......... equation 1

Since x+2 is a factor so
f (-2) = 0
2(-2)³ + m(-2)² + n(-2) - 14 = 0
-16 + 4m - 2n - 14 = 0
4m - 2n = 30
2m - n = 15........ equation 2

equation 1 + equation 2:
3m = 27
m = 9

from equation 1:
9 + n = 12
n = 3