Question

Wyznacz współczynnik a wielomianu w, jeśli: a) w(x)=ax`2 +x+1 , w(1)=3 b) w(x)= 3x'2 -x'2+a, w(3)=0 c) w(x)=x'3+ax'2+3, w(-4)=3 d) w(x)=ax'4+4x+2. w(2)=-6

Answer 1

a) w(x)=ax`2 +x+1 , w(1)=3

W(1)=a*1^2+1+1=3

a+2=3

a=3-2

a=1

b) w(x)= 3x'2 -x'2+a, w(3)=0

W(3)=3*3^2-3*3+a=0

27-9+a=0

a=18

c) w(x)=x'3+ax'2+3, w(-4)=3

w(-4)=(-4)^3+a*(-4)^2+3=3

-64+16a+3=3

16a=64/16

a=4

d) w(x)=ax'4+4x+2. w(2)=-6

w(2)=a*2^4+4*2+2=-6

16a+16+2=-6

16a=-24/16

a=-24/16

a=-3/2