(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For a cubic polynomial P(x), with real coefficients, P(2+i)=0, P(1)=0 and P(0)=10.

Express P(x) in the form P(x)=ax^3+bx^2+cx+d

and solve the equation P(x)=0

2. Relevant equations

The conjugate factor theorem

3. The attempt at a solution

Using remainder theorem

When P(2+i) = 0,

P(2+i)=a(2+i)^3+b(2+i)^2+c(2+i)+d

0=2a+3b+2c+d+11ai+4bi+ci

P(1)=0

0= a+b+c+d

P(0)=10

d=10

P(2-i)=0 <--- according to the conjugate theorem

P(2-i) =0

0= 2a+3b+2c+d-11ai-4bi-ci

I have trouble solving this through simultaneous equations. Is there another method?

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# Homework Help: Solving Complex Numbers

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