Question

Dany jest wielomian W(x)=(x^2 - 16)( 2x+ 6)(x - m). Jeśli iloczyn pierwiastków tego wielomianu 24, to:

A.m= -1/2

b.m= 1/2

c.m= -2

d.m= 2

dam naj ;)

Answer 1

W(x) = ( x^2 - 16)*( 2x + 6)*( x - m) =2* ( x - 4)*(x + 4)*( x + 3)*( x - m)

Mamy

x1 = 4, x2 = - 4, x3 = - 3

zatem

x1*x2*x3*x4 = 4*(-4)*(-3)*x4 = 24

48 x4 = 24  / : 48

x4 = 1/2

zatem

1/2 - m = 0

m = 1/2

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Odp. B

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