Question

wyznacz p i q wielomianu w(x)=-px^3+x^2+x-6q jesli w(-1)=4 i w(0)=3

Answer 1

W(x) = - p x^3 + x^2 + x - 6 q

 

W( - 1) = 4 , czyli  - p*( -1)^ 3 + ( -1)^2  - 1 - 6 q = 4

W( 0) = 3 , czyli     - p*0^3 + 0^2 + 0 - 6 q = 3

Mamy

p - 6 q = 4

 - 6q = 3

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

p + 3 = 4

q = - 1/2

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

p = 1

q = - 1/2

=========

 

Answer 2

W(x) = -px³+x²+x-6q

W(-1) = 4  i  W(0) = 3

 

-p·(-1)³+(-1)²+(-1)-6q = 4

-p·0³+0²+0-6q = 3

 

p+1-1-6q = 4

-6q = 3  /:(-6)

 

p-6q = 4  -> p = 4+6q

q = -½

=====

p = 4+6·(-½) = 4-3 = 1

p = 1

====