Question

Find the valur of a and b so that the polynomial (x^3 - 10x^2 +ax +b ) is exactly divisible by (x-1) as well as (x-2)

Answer 1

Heya !!!




( X -1) and ( X -2) are two factor of the given polynomial.




( X -1) = 0 --------------- ( X -2) = 0




X = 1 ------------------ X = 2





P(X) = X³ - 10X² + AX + B




P(1) = (1)³ - 10 × (1)² + A × 1 + B





=> 1 - 10 + A + B = 0





=> A + B = 9 ----------(1)



Also,


X = 2




P(2) = (2)³ -10 × (2)² + A × 2 + B




=> 8 - 40 + 2A + B = 0




=> 2A + B = 32 ---------(2)



From equation (1) we get ,



A + B = 9




B = 9 - A --------(3)



Putting the value of A in equation (2)





2A + B = 32




2A + 9 - A = 32




A = 32-9




A = 23





Putting the value of A in equation (3)




B = 9 - A




B = 9 - 23 = -14



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