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
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 $\displaystyle \displaystyle a \neq -b$, that means $\displaystyle \displaystyle -ai$ and $\displaystyle \displaystyle -bi$ are also roots.
Therefore $\displaystyle \displaystyle P(z) = \alpha(z - ai)(z + ai)(z - bi)(z + bi)$.
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