Question

Find the values of a and b so that the polynomial
x^3 - 10x^2 + ax + b is exactly divisible by (x - 1) as well as (x - 2).

Answer 1

Answer:

Step-by-step explanation:

Hello Mate!

Factor theorum states that p( x ) = 0

x = 1, 2

p( x ) = x^3 -10x^2+ax+ b

0 = 1 - 10 + a + b

0 = - 9 + a + b ------(1)

0 = 2^3 - 10(2)^2 + a(2) + b

0 = 8 - 40 + 2a + b

0 = - 32 + 2a + b ------(2)

(1) - (2)

-9 + a + b

-( - 32 + 2a - b )

23 - a = 0

a = 23

keeping value of a in eq. 1

0 = - 9 + 23 + b

-14 = b

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