## Algebra and Trigonometry 10th Edition

$f(x)=x^4+5x^2+4$
If $i$ is a zero of $f$ then the complex conjugate $-i$ is also a zero. If $2i$ is a zero of $f$ then the complex conjugate $-2i$ is also a zero. We have four zeros. We can find a four-degree polynomial. $f(x)=a[(x-i)[x-(-i)](x-2i)[x-(-2i)]$ $f(x)=a(x^2-i^2)[x^2-(2i)^2]$ $f(x)=a(x^2+1)(x^2+4)$ $f(x)=a(x^4+4x^2+x^2+4)$ $f(x)=a(x^4+5x^2+4)$ $a=1$ $f(x)=1(x^4+5x^2+4)$ $f(x)=x^4+5x^2+4$