# Thread: Polynomial

1. ## Polynomial

If P(z) is a polynomial of degree 4 with all its coefficients real with ai, bi as two of the zeros, then tern that does not contain z is:

can you guys please solve this i got no idea how to approach this

thanks

2. I'm not sure what you mean by "the term that does not contain z..."

Since the coefficients are all real, complex solutions occur as conjugates, so assuming $\displaystyle a \neq -b$, that means $\displaystyle -ai$ and $\displaystyle -bi$ are also roots.

Therefore $\displaystyle P(z) = \alpha(z - ai)(z + ai)(z - bi)(z + bi)$.

3. Originally Posted by Barney
If P(z) is a polynomial of degree 4 with all its coefficients real with ai, bi as two of the zeros, then tern that does not contain z is:

can you guys please solve this i got no idea how to approach this

thanks
Please post the question exactly as it's written in the source you got it from.

4. Exactly as the question says, and it a multiple choice:
If P(z) is a polynomial of degree 4 with all its coefficients real with ai, bi(a, b element R) as two of the zeros, then the term that does not contain z is:
Answers:
A) ab
B) a-b
C) a+b
D) a^3b^3
E) a^2b^2

5. I think it's asking for the value of the constant term.

Expand the expression I gave above...

6. Originally Posted by Barney
Exactly as the question says, and it a multiple choice:
If P(z) is a polynomial of degree 4 with all its coefficients real with ai, bi(a, b element R) as two of the zeros, then the term that does not contain z is:
Answers:
A) ab
B) a-b
C) a+b
D) a^3b^3
E) a^2b^2
Doesn't the problem also say that the polynomial is "monic" (coefficient of highest power is 1)? If the polynomial were not monic, none of those would be true.