given a factor, find the equation.
2+i, find the equation with lowest degree n

Question

given a factor, find the equation.
2+i, find the equation with lowest degree n

anonymous · Answer

@lgbasallote

anonymous · Answer

@vf321

anonymous · Answer

i know that it has degree 1, and in the book the answer is a(x-2-i), i don't understand why we also changed the 2+i.

anonymous · Answer

Okay.  you've got some things messed up.   2+i is a root for the polynomial x-(2+i) because the value of x = 2+ i makes the entire expression equivalent to zero.

anonymous · Answer

However, what I'm pretty sure you're looking for is, "What is the lowest-power polynomial WITH REAL COEFFICIENTS that has a root of 2+i?"  In that case, your answer cannot be x-(2+i) on its own because that polynomial has a complex coefficient - 2+i - on the x^0 term.  You have to add in another root that will "cancel out" the imaginary part.  Try to CONJecture another root.

anonymous · Answer

it didn't say anything about real roots in the book.. and the answer is a(x-2-i), i don't understand what you are talking about..