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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
answered-by-expert 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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