Algebra and Applications Test 3

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Question : 20 of 25

Marks: +1, -0

If

z ^3 + bz + c

and

b^3 + cz + b

have a common factor which one of the following is correct?

b + c - 1 = 0
b + c = 0
b + c + 1 = 0
b - c +1 = 0
None of these

Solution:

Let z - σ is a common factor to

z^3 + bz + c

and

z^3 + cz + b

.

σ^3 + bσ + c = 0

and

σ^3 + cσ + b = 0

From (i) and (ii)

bσ - cσ = c - b

⇒ σ = -1

∴ from (i)

-1 - b + c = 0

b - c + 1 = 0

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