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Further Maths GCSE Help

A function, f , is such that f(x) = x^4-2x^2+1 .
(i) Solve the equation f(x)=0 giving all solutions in their exact form.

(ii) Find the coordinates of the stationary points of the curve y=f(x) .

I think I factorised the top one correctly getting
(x-1)(x+1)(x-1)(x+1)
so x is 1 or -1 but is this all you have to do

Then for the second part I differentiated it to get

4x^3-4x = 0 (because the gradient is 0)
and by using factor theorem I worked out that x=1 is an x value and so when you put that back into the original equation you get y as 0 but is this all you have to do, I know how to factorise regular cubics but can't quite get my head around this .
Thanks
4x^3 -4x =0 has 4x in both terms, so you can factorise to 4x(x^2 +1) this then factorises to 4x(x+1)(x-1) to give x=0, x=1 or x=-1, I believe
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zara_ruby
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Original post by TheVirtualPhoton
4x^3 -4x =0 has 4x in both terms, so you can factorise to 4x(x^2 +1) this then factorises to 4x(x+1)(x-1) to give x=0, x=1 or x=-1, I believe


Ok thanks but If you expand the part in bold then you will get x^2-1 instead of x^2+1 which is underlined
Sorry I meant it first factorises to 4x(x^2 -1), not x^2 +1
Original post by zara_ruby
Ok thanks but If you expand the part in bold then you will get x^2-1 instead of x^2+1 which is underlined


I think they meant 4x(x^2 - 1) where they underlined.

Edit: Ghosted :lol:

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