Question

zapisz wielomiany w postaci iloczynowej i wyznacz pierwiastki wielomianu a)W(x)=(x²-3x)(4x²+5x+1) b)W(x)=x³+x²-4x-4

Answer 1

a)

W(x) = ( x^2 - 3 x)*( 4 x^2 + 5 x + 1)= x*( x - 3) *4*( x + 1)*( x + 1/4) =

= 4x*( x - 3)*(x + 1)*( x + 1/4)

=============================

bo

 

delta = 5^2 - 4*4*1 = 25 - 16 = 9

p(delty) = 3

x = [ - 5 - 3]/ 8 = - 1    lub   x = [ - 5 + 3]/ 8 = - 1/4

-----------------------------------------------------------------------------------------

Pierwiastki:   x1 = - 1,  x2 =  -1/4,  x3 = 0,  x4 = 3

=======================================================

b)

W(x) = x^3 + x^2 - 4 x - 4 = x^2 *( x + 1) - 4*( x + 1) = ( x + 1)*( x^2 - 4) =

= ( x + 1)*( x - 2)*(x + 2)

===========================

Pierwiastki:  x1 = - 2,  x2 = - 1,  x3 = 2

=========================================