Using the given zero, find all other zeros of f(x).

-2i is a zero of f(x) = x^4 - 32x^2 - 144

Question

Using the given zero, find all other zeros of f(x).

-2i is a zero of f(x) = x^4 - 32x^2 - 144

anonymous · Answer

@satellite73 @amistre64

anonymous · Answer

@ganeshie8

anonymous · Answer

since $-2i$ is a zero, so is its conjugate $+2i$ and you can now put out two factors 
$$(x-2i)(x+2i)=x^2+4$$

anonymous · Answer

that makes 
$$x^4 - 32x^2 - 144=(x^2+4)(\text{something})$$ and you can find the something  by division or by thinking

anonymous · Answer

can Iuse synthetic division? with -4?

anonymous · Answer

alternatively you can write 
$$ x^4 - 32x^2 - 144=u^2-32u-144$$ where $u=x^2$
first solve for $u$ then for $x$

anonymous · Answer

no you cannot

anonymous · Answer

because it is $x^2+4$ not $x+4$ 
synthetic division will not work here because of the $x^2$ term

anonymous · Answer

ohh okay then how would I solve for u and x?

anonymous · Answer

$$u^2-32u-144=0\
(u+4)(u-36)=0\
u=-4,u=36$$

anonymous · Answer

then $$x^2=-4,x^2=36$$ making 
$$x=\pm2i,x=\pm6$$

anonymous · Answer

alternatively you can skip the substitution and write 
$$x^4-32x-144=(x^2+4)(x^2-36)$$ and solve that one 
same thing

anonymous · Answer

so it's just 2i, 6, -6?

anonymous · Answer

yes, and also $-2i$

anonymous · Answer

it is a polynomial of degree 4, how many zeros did you expect?