Question

need some help please?

Answer 1

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

Answer 2

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

Answer 3

Hello?

Answer 4

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

Answer 5

Sorry! Yeah I can

Answer 6

I had \[(x+4) and (x-2)^2\]

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

remember you have:\[p(x)=(x+4)(x-2)^2\]

Answer 11

Ermm okay I got \[\pm2i\] as two imaginary roots

Answer 12

those are just two of the roots

Answer 13

and \[\pm \sqrt{2}\]

Answer 14

correct :)

Answer 15

\[p(x) = (x+4)(x-2)^2\]
\[p(x^2) = ((x^2)+4)((x^2)-2)^2\]


\[((x^2)+4) = 0\]
\[((x^2)-2)^2 = 0\]
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

Answer 16

lol thanks :)