anonymous
  • anonymous
need some help please?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
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
  • austinL
Put in x^2 for all instances of x, and then set it equal to zero.
austinL
  • austinL
Hello?

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asnaseer
  • asnaseer
try to first factorise p(x) - can you do that @Obumpa ?
anonymous
  • anonymous
Sorry! Yeah I can
anonymous
  • anonymous
I had \[(x+4) and (x-2)^2\]
asnaseer
  • asnaseer
correct - now replace each x in this expression with \(x^2\) and set the whole thing to equal zero as suggested by @austinL
anonymous
  • anonymous
@austinL I tried that wasn't really working /:
asnaseer
  • asnaseer
what expression do you get for \(p(x^2)\) ?
asnaseer
  • asnaseer
remember you have:\[p(x)=(x+4)(x-2)^2\]
anonymous
  • anonymous
Ermm okay I got \[\pm2i\] as two imaginary roots
asnaseer
  • asnaseer
those are just two of the roots
anonymous
  • anonymous
and \[\pm \sqrt{2}\]
asnaseer
  • asnaseer
correct :)
austinL
  • austinL
\[p(x) = (x+4)(x-2)^2\] \[p(x^2) = ((x^2)+4)((x^2)-2)^2\] \[((x^2)+4) = 0\] \[((x^2)-2)^2 = 0\] 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
  • anonymous
lol thanks :)

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