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$P(x)$ 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 $Q(x)$.

 Dec 28, 2020

Best Answer 

 #1
avatar+32013 
+3

Q(2+i) = a(2+i) + b = 2a+b + ai

Since Q(2+i) = P(2+i) we must have 2a+b + bi = 4 - 3i

 

Equate real and imaginary parts
Real:  2a + b = 4

Imag: b = -3

 

I'll leave you to finish this.

 Dec 29, 2020
 #1
avatar+32013 
+3
Best Answer

Q(2+i) = a(2+i) + b = 2a+b + ai

Since Q(2+i) = P(2+i) we must have 2a+b + bi = 4 - 3i

 

Equate real and imaginary parts
Real:  2a + b = 4

Imag: b = -3

 

I'll leave you to finish this.

Alan Dec 29, 2020

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