5. If x3+ax2 -bx +10 is divisible by x2 -3x+2, find the values of a and b.
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Step-by-step explanation:
(x³-3x+2) = (x-1)(x-2)
(x - 1) & (x - 2) is the factors of
x³ + ax² - bx + 10 = 0
Firstly ,when x = 1
(1)³ + a(1)² - b(1) + 10 = 0
a - b = -11 --------(1)
& , when x = 2
(2)³ + a(2)² - b(2) + 10 = 0
8 + 4a - 2b + 10 = 0
4a - 2b = -18
2a - b = -9 ---------(2)
from eq. (2) - (1)
a = -9 + 11
a = 2
b = a + 11
b = 2+11
b = 13
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