Show that the polynomial f(x) = x^{4} + 4x^{2} + 6 has no zero.

Let us assume t = x^{2}

∴ f (t) = t^{2} + 4t + 6

Now first of all we have to equate f (t) = 0 in order to find the zeros

∴ t =

=

= - 2

As, t = x^{2}

So, x^{2} = - 2

x =

We know that, the zeros of the polynomial should be a real number and this is not a real number

∴ f (x) hs no zeros

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