Question

Dobierz wartość m tak, aby liczba -2 była pierwiastkiem wielomianu
W(x) = x(do potęgi 4) + mx³ - 3x²+ (m²+4)x-2.

Answer 1

W(-2) = 0

W(-2) = (-2)^4 + m * (-2)^3 - 3 * (-2)^2 + (m^2 + 4) * (-2) - 2

W(-2) = 16 - 8m - 12 - 2(m^2 + 4) - 2

W(-2) = 2 - 8m - 2m^2 - 8

 

-2m^2 - 8m - 6 = 0

m^2 + 4m + 3 = 0

Δ = 16 - 12 = 4

√Δ = 2

m1 = (-4 - 2) / 2 = -6/2 = -3

m2 = (-4 + 2) / 2 = -2/2 = -1

 

odp. m = -3 lub m = -1

Answer 2

W(-2) = (-2)⁴ + m*(-2)³ - 3*(-2)² + (m²+4)*(-2) - 2 = 16 - 8m -12 -2m²-8 - 2 

 

       -2m²-8m - 6 = 0

Δ=64 - 48 = 16

√Δ = 4

 

m1 = (8-4)/-4 = 4/-4 = -1

m2=(8+4)/-4 = 12/-4 = -3

odp:

m=-1  U  m=-3