Determine the values of a and b for which the polynomial x^3 +10^2+ax+b is exatly divisible by (x-1)as well as(x-2)
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polynomial , x³ +10x² + ax + b is exactly divisible by ( x -1) and (x -2)
it means x = 1 and 2 are the zeors of given polynomial .
so, put x = 1
(1)³ + 10(1)² +a(1) + b = 0
1 + 10 + a + b = 0
a + b = -11 --------(1)
again put x =2
(2)³ +10(2)² +a(2) + b =0
8 + 40 + 2a + b = 0
2a + b = -48 ----------(2)
solve equations (1) and (2)
a = -37
b = 26
it means x = 1 and 2 are the zeors of given polynomial .
so, put x = 1
(1)³ + 10(1)² +a(1) + b = 0
1 + 10 + a + b = 0
a + b = -11 --------(1)
again put x =2
(2)³ +10(2)² +a(2) + b =0
8 + 40 + 2a + b = 0
2a + b = -48 ----------(2)
solve equations (1) and (2)
a = -37
b = 26
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