Question

find the value of a and b so that the polynomial p(x)= x^3 - 6x^2 - ax - b is exactly divisible by both (x-1) and (x-2)
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Answer 1

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

Hope dis helps

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