Question

x^4 =2x^2=1
Factor completely and find all zeros, real and complex

Answer 1

Do you mean x^4 + 2x^2 + 1? @middi1997

Answer 2

yes

Answer 3

can you help

Answer 4

Let's first factor:\[x^4+2x^2+1=(x^2+1)^2\] It's pretty obvious that the function has no real zeroes so it must have complex zeroes. So let's set it to 0 and find out:\[(x^2+1)^2 = 0 \implies x^2+1 = 0 \implies x = \pm i\] So the function has no real zeroes and has complex zeroes for \(\pm\bf i\).

@middi1997

Answer 5

thank you so much is there anything I can help you with like your smart score

Answer 6

ok and how did you know to make it (x^2+1)^2

Answer 7

Think of it like this. Set u = x^2. So our function becomes:\[x^4+2x^2+1=u^2+2u+1=(u+1)^2=(x^2+1)^2\] Get it? Just factor the way you would factor quadratics by replacing x^2 with u and then putting it back after you've factored.

Answer 8

ok thank you :)

Answer 9

No problem.