Answer to Question #88935 in Abstract Algebra for RAKESH DEY

Question

A linear equation over R can have at most one root in C\R.
Is the statement true or false? Justify your answer.

Answer 1

The statement is false. A linear equation can have one root, infinitely many roots, or no roots: 1) a linear equation has a single root if the variable multiplier is not zero. 2) the linear equation has infinitely many roots if the multiplier for the variable and the free term of the equation are zero.3) the linear equation has no roots if the multiplier for the variable is zero and the free term of the equation is not zero.