>>Hey! So I couldn't really understand this question and how to solve it... could anyone help me here?
P(x) is a polynomial with real coefficients such that P(2+i)=4-3i
There is a linear function Q(x)= ax+b with real coefficients such that Q(2+i)=P(2+i).
Find Q(x). Make sure to express your answer in the form ax+b.
Thanks! I would appreciate an explanation too, if you could! :)
P(2 + i) = 4 - 3i
Q(2 + i) = P(2 + i)
Which implies that
Q(2 + i) = 4 - 3i
And Q (x ) = ax+ b
Q ( 2 + i) = a (2 + i) + b = 2a +ai + b
2a + ai + b = 4 - 3i
So.....this implies that
(2a + b) + ai = 4 - 3i equate co-efficients
2a + b = 4
a = - 3
2(-3) + b = 4
-6 + b = 4
b = 10
Q(x) = -3x + 10
Q(2 + i) = -3(2 + i) + 10 = -6 - 3i + 10 = 4 - 3i
Wow! Thanks so much! I finally get it now. This was a big help for me. Thanks especially for doing it so quickly! :)
No prob....every now and then I manage to get one correct....LOL!!!
BTW....welcome aboard !!!