Show that the polynomial f(x)= x^4+4x^2 +6 has no zeros

1.	Show that the polynomial f(x)= x^4+4x^2 +6 has no zeros
Answer» f(x) = x4\xa0+ 4x2\xa0+ 6= (x2)2\xa0+ 4x2\xa0+ 6Let x2\xa0=n,Then, f(x) = n2\xa0+ 4n + 6,Here a=1,b=4,c=6The discriminant(D) = {tex}\\text{b}^2-4\\mathrm{ac}=\\;(4)^2-4\\times1\\times6=16-24=-8{/tex}Since the discriminant is negative so this polynomial has no zerosHence, f(x) = x4\xa0+ 4x2\xa0+ 6 has no zero.

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