Question

escreva a forma ax4+bx2+cx+d= 0 cujas raízes são:
a)2,3,4 e 5
b)-2,3,4 e -5
c) 1,0,3 e 7​

Answer 1

A) 2, 3, 4 e 5

S₁ = 2+3+4+5 = 14

S₂ = 2.3 + 2.4 + 2.5 + 3.4 + 3.5 + 4.5 =

6 + 8 + 10 + 12 + 15 + 20 = 71

S₃ = 2.3.4 + 2.3.5 + 2.4.5 + 3.4.5 =

24 + 30 + 40 + 60 = 154

S₄ = 2.3.4.5 = 120

x⁴ - 14x³ + 71x² - 154x + 120 = 0

B) -2, 3, 4 e -5

S₁ = -2+3+4-5 = 0

S₂ = -2.3 + (-2).4 + (-2).(-5) + 3.4 + 3.(-5) + 4.(-5) =

-6 + (-8) + 10 + 12 + (-15) + (-20) = -27

S₃ = -2.3.4 + (-2).3.(-5) + (-2).4.(-5) + 3.4.(-5) =

-24 + 30 + 40 + (-60) = -14

S₄ = -2.3.4.(-5) = 120

x⁴ - x³ - 27x² + 14x + 120 = 0

C) 1, 0, 3 e 7

S₁= 1 + 0 + 3 + 7 = 11

S₂= 1.0 + 1.3 + 1.7 + 0.3 + 0.7 + 3.7 =

0 + 3 + 7 + 0 + 0 + 21 = 31

S₃= 1.0.3 + 1.0.7 + 1.3.7 + 0.3.7 =

0 + 0 + 21 + 0 = 21

S₄= 1 . 0 . 3 . 7 = 0

x⁴ - 11x³ + 31x² - 21x = 0