Question

o polinômio p(x) = x³-ax²+bx admite raízes 6 e 1 calcule os coeficientes a e b

Answer 1

$x^3-ax^2+bx\\ \\ 6^3-a(6)^2+b(6)\\ 216-36a+6b\quad (:6)\\ \\ 36-6a+b\\ -6a+b=-36\\ \\ 1^3-a(1)^2+b(1)\\ 1-a+b\\ -a+b=-1\\ \\ -6a+b=-36\quad (-1)\\ -a+b=-1\quad \\ \\ 6a-b=36\\ -a+b=-1\\ \\ 5a=35\\ a=\frac { 35 }{ 5 } \\ a=7\\ \\ -7+b=-1\\ b=-1+7\\ b=6\\ \\ x^3-7x^2+6x$