Question

dado o polinômio p(x)=2x3-6x2+mx+n,se p(2)=o e p(-1)=-6. calcule m e n

Answer 1

p(x) = 6x - 12x + mx + n

p(2) = 6 . 2 - 12 . 2 + 2m + n
p(2) = 12 - 24 + 2m + n
p(2) = 2m + n - 12

2m + n - 12 = 0
n= 12 - 2m

p(-1) = 6 . (-1) - 12 . (-1) - m + n
p(-1) = - 6 + 12 - m + n
p(-1) = - m + n + 6

 - m + n + 6 = 6
- m = - n          // MULTIPLICA   POR     (-1)
m = n



n= 12 - 2m
n = 12 - 2n
3 n = 12
n = $\frac{12}{3}$
n= 4

m = n
m = 4

Answer 2

p(x)=2x3-6x2+mx+n
p(2)=o
p(-1)=-6

 2x3-6x2+mx+n ==> 2(2)^3-6(2)^2 +2m + n = 0 ==> 2m + n = -16+24
2x3-6x2+mx+n ==> 2(-1)^3-6(-1)^2 - m + n = 0 ==> - m + n = 2+ 6


2m + n = 8 ==>   2m + n = 8
-m + n = 8(2)=>  -2m+2n = 16
                                    3n = 24 ==> n = 8 

 2m + n = 8 ==> 2m = - 8 + 8 ==> m = 0