Q16 of 113 Page 71

Show that the polynomial f(x) = x4 + 4x2 + 6 has no zero.

Let us assume t = x2

∴ f (t) = t2 + 4t + 6


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


∴ t =


=


= - 2


As, t = x2


So, x2 = - 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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