Question

Given that (x + 1) and (x - 2) are factors of r + ar- bx - 6, find the values of a and b. With
values of a and b, factorise the given expression completely..
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Answer 1

Answer:

f(x)=x3+ax2+bx+6

(x−2) in a factor ⇒f(2)=0

f(2)⇒23+a(2)2+2b+6=0

⇒8+4a+2b+b=0

⇒4a+2b+14=0

⇒2a+b+7=0 -(1)

f(x−3)=3 (Remainder)

⇒f(3)⇒33+a(3)2+b×3+6=3

⇒27+9a+3b+b=3

⇒9a+3b+30=0

⇒3a+b+10=0 _____ (2)

From (1) & (2)

b=−2a−7 & b=−10−3a

−2a−7=−10−3a

3a−2a=−10+7

a=−3

from (3)

b=−2(a)−7=2(−3)−7

   =6−7

b=−1

answer