CBSE Class 9 Answered
Find
the values of a and b so that (x + 1) and (x - 2) are factors of (x3
+ ax2 + 2x + b).
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
Expert Answer
If (x + 1) is a factor of x3 + ax2 + 2x + b then
(-1)3 + a(-1)2 + 2(-1) + b = 0
-1 + a - 2 + b = 0
a + b = 3 ...(1)
If (x - 2) is a factor of x3 + ax2 + 2x+ b then
(2)3 + a(2)2 + 2(2) + b = 0
4a + b = -12 ...(2)
Subtracting (1) from (2), we get
3a = -15
Or, a = -5
Using in (1), we get
-5 + b = 3
Or, b = 8
Hence, a = -5, b = 8.
Answered by | 04 Jun, 2014, 03:23: PM
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