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ICSE Class 10 Answered

(x-3) is a factor of x to the power 3 + ax to the power 2+ bx - 9 and when it is divided by (x - 2) the remainder is 1
Asked by kushalsahu20march | 16 May, 2019, 11:56: AM
Expert Answer
Let p(x) =x3 + ax2 + bx - 9
(x-3) is a factor of x3 + ax2 + bx - 9 .. given
 
→ p(3) = 0

→ (3)3 + a(3)2 + b(3) - 9 = 0
 
→ 27 + 9a + 3b - 9 = 0

→ 3a + b = -6  ... (i)
 
 
when p(x) is divided by (x - 2) the remainder is 1  ... given
 
→ p(2) = 1 
 
→  (2)3 + a(2)2 + b(2) - 9 = 1
 
→  4a + 2b = 2   
→  2a + b = 1   .... (ii)
 
Solving (i) and (ii), we get
 
a = -7 and b = 14 

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