Polynomial - common factor (1 Viewer)

[airie]

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]

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]

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

 

[airie]

So you mean the question's wrong?

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