Try out this beautiful algebra problem from AMC 8, 2019 based on the Fundamental Theorem of Algebra
How many different real numbers satisfy the equation
But try the problem first...
Answer: is (D) 4
AMC 8, 2019, Problem 20
The given equation is
and that means
Among both cases, if
and that means we have 2 different real numbers that satisfy the equation.
and if we take another case, then
and that means we have 2 different real numbers in this `case too that satisfy the equation. So total 2+2=4 real numbers that satisfy the equation.