Question

expression x^3 +px^2 -x+q is completely divided by (x+1) and (x+ 2) find the values of p and q​

Answer 1

Answer:

f(x) = x^3 +px^2 - x +q

If f(x) completely divided by (x+1) and (x+2) then,

f(-1) =0   and

f(-2)=0

f(-1) = 0

-1^3 + p -1^2 - (-1) + q = 0

-1 + p +1 + q = 0

p + q = 0

p=-q

f(-2) = 0

-2^3 + p*-2^2 - (-2) + q = 0

-8 + 4p +4 + q = 0

4p + q = 4

putting p = -q here

-4q + q = 4

-3q=4

q = -4/3

p=-q

p = 4/3

Your answer is p  = 4/3 and q = -4/3

Step-by-step explanation:

Hope it helps :-)