if x3 + ax2 - bx +10 is divisible by x2-3x+2 find the value of A and B
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Step-by-step explanation:
x3 + a x2 – bx + 10 is divisible by x2 – 3 x + 2
Factors of x2 – 3 x + 2 are (x - 1) (x - 2)
Hence, f(1) = 0
1 + a - b + 10 = 0
a - b = - 11..........(i)
f(2) = 0
23 + 22 a - 2b + 10 = 0
8 + 4a - 2b = -10
4a - 2b = - 18
2a - b = -9..........(ii)
Subtracting (i) from (i)
a - 2a - b + b = -11 + 9
-a = -2
a = 2
Consider,
a - b = -11
2 - b = -11
2 + 11 = b
b = 13
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