need some help please?

Question

anonymous · Answer

The polynomial p(x) is defined by$$p(x)=x^3 −12x+16$$  i) find all the roots of the equation so$$ p(x^2) = 0$$

austinl · Answer

Put in x^2 for all instances of x, and then set it equal to zero.

austinl · Answer

Hello?

asnaseer · Answer

try to first factorise p(x) - can you do that @Obumpa ?

anonymous · Answer

Sorry! Yeah I can

anonymous · Answer

I had $$(x+4) and (x-2)^2$$

asnaseer · Answer

correct - now replace each x in this expression with $x^2$ and set the whole thing to equal zero as suggested by @austinL

anonymous · Answer

@austinL I tried that wasn't really working /:

asnaseer · Answer

what expression do you get for $p(x^2)$ ?

asnaseer · Answer

remember you have:$$p(x)=(x+4)(x-2)^2$$

anonymous · Answer

Ermm okay I got $$\pm2i$$ as two imaginary roots

asnaseer · Answer

those are just two of the roots

anonymous · Answer

and $$\pm \sqrt{2}$$

asnaseer · Answer

correct :)

austinl · Answer

$$p(x) = (x+4)(x-2)^2$$
$$p(x^2) = ((x^2)+4)((x^2)-2)^2$$


$$((x^2)+4) = 0$$
$$((x^2)-2)^2 = 0$$
Then you can solve for x in each one.

I believe you have already arrived there... however, I have typed out this whole answer and do not want to waste all my effort. :P

anonymous · Answer

lol thanks :)