Question

x^4-4x^2+k.
Solve individually for k that make the statements true.
a. 4 real zeros
b. 4 imaginary zeros
c. 2 real zeros, 2 imaginary roots
d. 2 real zeros, each w/ multiplicity of 2
I don't even know how to start.

Answer 1

here is a nice graph of
\[x^4-4x^2\] now you can raise it and lower it to get what you want.
at present it has 3 zeros, -2,0,2 and 0 has multiplicity 2

Answer 2

http://www.wolframalpha.com/input/?i=x^4-4x^2

Answer 3

so to get 4 imaginary zeros, just lift it way up so it sits totally above the x - axis

Answer 4

say
\[x^4-4x^2+20\] would probably do it

Answer 5

4 real zeros have to lift it up a little so it crosses the x - axis 4 times
probably
\[x^4-4x^2+2\] would work
http://www.wolframalpha.com/input/?i=x^4-4x^2%2B2