Question

1. Wyznacz współczynniki a i b wielomianu W(x)= + ax+ b tak,aby W(-1)=2 i W(2)=-31.

2.Wyznacz współczynniki a i b wielomianu W(x)= + +x +b tak,aby W(1)=-5 i W(-1)=-1.

Answer 1

) W(-1)= 5-a+b

  W(2)= -40+4a+b

2=5-a+b

-31=-40+4a+b

b= a+3

9=4a+a+3

6=5a a=6/5

b= 6/5+3= 21/5

2) W(1)= 2+a+1+b

w(-1)= -2-a-1+b

-5=3+a+b

-1=-3-a+b

b= -8-a -1=-3-a-8-a

10=-2a

a=-5

b=-3

 

Answer 2

W(x)=-5x³+ax+b             W(-1)=2  i W(2)=-31

  

                  -5(-1)³+(-1)a+b=2

                   -5·2³+ 2a+b=-31

 

                  5-a+b=2

                  -40+2a+b=-31

 

                   b-a=-3

                   2a+b=40-31=9

 

                  b=a-3

                  2a+(a-3)=9

                  3a=9+3=12

                    a=12/3=4

                    b=4-3=1

 

                    a=4,   b=1

 wzór wielomanu  W(x)=5x³+4x+1

 

2/  W(x)=2x⁴+ax³+x+b  W(1)=-5   W(-1)=-1

 

                      2·1⁴+1³a+1+b=-5

                      2·(-1)⁴+(-1)³a -1+b=-1

 

                     2+a+1+b=-5

                     2-a-1+b=-1

 

                    a+b=-5-2-1=-8

                   - a+b=-1+1-2=-2

 

                        a=-8-b

                       -(-8-b)+b=-2

 

                        a=-8-b

                        8+b+b=-2

 

                        a=-8-b

                        2b=-2-8=-10

 

                         b=-10/2=-5

                         a=-8-(-5)=-8+5=-3

 

                         a=-3,      b=-5

 

W(x)= 2x⁴-3x³+x-5