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Polynomial - common factor (1 Viewer)

airie

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From Cambridge (year 12 textbook), Exercise 4E, Q14:

Show that if the polynomials x3+ax2-x+b and x3+bx2-x+a have a common factor of degree 2, then a+b=0.

How do you do it? I bashed around for a bit and only managed to get a=b, which obviously works.

Thanks in advance :)
 

jyu

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airie said:
From Cambridge (year 12 textbook), Exercise 4E, Q14:

Show that if the polynomials x3+ax2-x+b and x3+bx2-x+a have a common factor of degree 2, then a+b=0.

How do you do it? I bashed around for a bit and only managed to get a=b, which obviously works.

Thanks in advance :)
a - b = 0 is the correct answer.
 

haque

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Although cambrideg would have few mistakes it would appear they have made a mistake here(typo) a=b is the condtion imo
 

airie

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So you mean the question's wrong?

Heh. Why do I always get stuck on questions with mistakes in them :eek:
 

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