Question

seja p (x)= 2x(a terceira) -6x(ao quadrado) +mx+n. Se p (2)=0 e p (-1)= -6 calcule os valores de m e n

Answer 1

$P(x) = 2 x^{3} -6 x^{2} +mx+n \\ \\ P(2)=0: 2 (2)^{3} -6 (2)^{2} +2m+n =0 \\ \\ 16-24 +2m+n=0: 2m+n=8 \\ \\ P(-1)=-6: 2 (-1)^{3} -6 (-1)^{2} +(-1)m+n =-6 \\ \\ -2+6-m+n=-6: -m+n=-10 \\ \\ \left \{ {2m+n=8} \atop {-m+n=-10}} \right. \\ \\ \left \{ {2m+n=8} \atop {-2m+2n=-20}} \right. \\ \\ 3n=-12; n = -4. \\ \\ -m+n=-10 \\ \\ -m-4=-10 -m=-6 \\ \\ m=6$