Question

If x^3+ax^2-bx+10 is divisible by x^2-3x+2 find the values of a and b. ​

Answer 1

Answer:

since x^2 - 3x + 2 = (x-2)(x-1)

so x^3 + ax^2 -bx + 10 must be divisible by both

x-2 and x-1

let f(x) = x^3 + ax^2- bx + 10

f(2) = 5 + 4a - 2b + 10 = 0 ---> 4a - 2b = -15

f(1) = 1 + a - b + 10 ---> a-b = -11 or a = b-11

sub 2nd into 1st

4(b-11) - 2b = -15

4b - 44 - 2b = -15

2b = 29

b = 29/2

then a = 29/2 - 11 = 7/2

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