State the number of complex roots, the possible number of real and imaginary roots, and the possible rational roots for each equation. Then find all roots. x^4-3x^2+2=0

Answer 1

let y=x^2, then y^2 -3y + 2 = 0

factor

(y-1)(y-2) = 0

y = 1,2

x = plus or minus square root of y = 1,-1, sqr2, -sqr2

4 real solutions,

by Descartes' rule of signs there are 2 sign changes, so either 0 or 2 possible positive real solutions

and 0 or 2 negative real solutions

possible 0, 2 or 4 imaginary solutions

as it turns out there are 2,2 and 0 +,- and imaginary roots, solutions, zeros or x intercepts

try a graphing calculator, the graph crosses or touches the x axis 4 times