Question

the polynomial P(X) is =x^4-2x^3+3x^2-ax+b when divide by( x+1) and (x-1) the remainder 5 and 19 respectively find value of a and b​

Answer 1

Answer:

a = -9, b = 8

Step-by-step explanation:

P(X) is =x^4-2x^3+3x^2-ax+b

(by remainder theorem)

P(-1) = 5

5= 1 - 2(-1) + 3(1) + a + b

5 = 1 + 2 + 3 +a + b

-1 = a +b ------- eqn 1

(by remainder theorem)

P(1) = 19

19 = 1 - 2 + 3 -a +b

19 - 2 = b - a

17 = b - a ------------eqn2

eqn1 + eqn2

-1 + 17 = 2b

16 = 2b

8 = b

substituting b in eqn1

-1 = a + 8

a = -9

hope it helps :)