CBSE Class 9 Answered
Find
the value of a and b so that the polynomial x3 + 10x2 +
ax + b has (x - 1) and (x + 2) as factors.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
Expert Answer
Let f(x) = x3 + 10x2 + ax + b
Since (x - 1) is a factor therefore
f(1) = 0
1 + 10 + a + b = 0
a + b = -11 … (1)
Also, (x + 2) is a factor, therefore
f(-2) = 0
(-2)3 + 10(-2)2 + a(-2) + b = 0
-8 + 40 -2a + b = 0
2a - b = 32 … (2)
Adding (1) and (2), we get
3a = 21
Or, a = 7
From (1), we get b = -11 - 7 = -18.
Hence, a = 7, b = -18.
Answered by | 04 Jun, 2014, 03:23: PM
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