Polynomial equations

[macostar]

Any help with this would be greatly appreciated. No matter what I do I cant get the real values for A and B.

[Zealous]

Any help with this would be greatly appreciated. No matter what I do I cant get the real values for A and B.

if P(2)=0 and P(1-i)=0, then (z-2) and (z-1+i) are factors of P(z).

As all the coefficients of z in P(z) are real numbers, we can use the conjugate root theorem and hence (z-1-i) must also be a factor.

We can now express P(z) as:



Expand:



Therefore a=4 and b=6.

The question asks for full working, so you'd need to show more working when expanding.


Another method (I like the first one better though):

Spoiler

Subbing in z=2


Subbing in z=1-i


You can then use simultaneous equations to solve for a and b, equating real and imaginery components.

[macostar]

Thanks for that Zealous big help.