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I f space left parenthesis space x squared plus a x squared plus b x plus 6 right parenthesis space h a s space left parenthesis space x minus 2 right parenthesis space a s space a space f a c t o r space a n d space l e a v e s space a space r e m i a n d e r space 3 space w h e n space d i v i d e d space b y space left parenthesis x minus 3 right parenthesis space comma space t h e n space f i n d space t h e space v a l u e space o f space space a space space a n d space space b.
Asked by kishor.kp14 | 19 Jun, 2019, 09:49: AM
answered-by-expert Expert Answer
When f(x) = x2  + ax2 + bx + 6 is divided by (x - 3) leaves a remainder 3.
 
→ f(3) = 3            ... By remainder theorem
→ (3)2  + a(3)2 + b(3) + 6 = 3
→ 9 + 9a + 3b + 6 = 3
→  9a + 3b + 15 = 3
→  9a + 3b  = -12 
Dividing both the sides by 3, we get
→  3a + b  = -4  .... (i)
 
(x - 2) is a factor of f(x)... given
→ x = 2  
f(2) = 0  ..... By factor theorem
→x2  + ax2 + bx + 6 = 0
→(2)2  + a(2)2 + b(2) + 6 = 0
→ 4 + 4a + 2b + 6 = 0
→ 4a + 2b  = -10   
Dividing both the sides by 3, we get 
→ 2a + b  = -5   ... (ii)
Subtracting (ii) from (i), we get
a = 1
Put a = 1 in (ii), we get
2(1) + b  = -5 
→ b = -7


Answered by Yasmeen Khan | 19 Jun, 2019, 10:15: AM

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