Hi all!

This should be a quick question.

if f is an irreducible polynomial (on the real line) of degree two, i need to show that it can be written in the form f(x)= (x - a)^2 + b^2

where a, and b lie on the real line and b is non-zero.

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so, I know that irreducible polynomials have no real solutions...

do I just assume f(x) can be written as x^2 + p*x+ q then complete the square and fudge it onto the expression above?

or do i need to use eucledian division?

many thanks