Question

5) Sendo as raízes R 1 , R 2, R 3 e R 4 igual a – 2, – 3, 1 e 3, determine: a) A equação polinomial na forma fatorada (X – R 1 ).(X – R 2 ).(X – R 3 ).(X – R 4 ) = 0 b) A equação polinomial na forma X 4 – S 1. X 3 + S 2. X 2 – S 3. X + P = 0 6)Dadas as raízes – 1, 2 e 3 , determine a equação X 3 – S 1. X 2 + S 2. X – P = 0

Answer 1

Explicação passo-a-passo:

5)

a)

$\sf [x-(-2)]\cdot[x-(-3)]\cdot(x-1)\cdot(x-3)=0$

$\sf (x+2)\cdot(x+3)\cdot(x-1)\cdot(x-3)=0$

b)

$\sf S_1=-2-3+1+3$

$\sf S_1=-1$

$\sf S_2=(-2)\cdot(-3)+(-2)\cdot1+(-2)\cdot3+(-3)\cdot1+(-3)\cdot3+1\cdot3$

$\sf S_2=6-2-6-3-9+3$

$\sf S_2=-11$

$\sf S_3=(-2)\cdot(-3)\cdot1+(-2)\cdot(-3)\cdot3+(-2)\cdot1\cdot3+(-3)\cdot1\cdot3$

$\sf S_3=6+18-6-9$

$\sf S_3=9$

$\sf P=(-2)\cdot(-3)\cdot1\cdot3$

$\sf P=18$

$\sf x^4+x^3-11x^2-9x+18=0$

6)

$\sf S_1=-1+2+3$

$\sf S_1=4$

$\sf S_2=(-1)\cdot2+(-1)\cdot3+2\cdot3$

$\sf S_2=-2-3+6$

$\sf S_2=1$

$\sf P=(-1)\cdot2\cdot3$

$\sf P=-6$

$\sf x^3-4x^2+x+6=0$