What are the real zeros of $f(x) = 3x^6 + 1$ ?

Question

4940 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-27T18:26:32

Refer to explanation

There aren't any. Let assume that there is value $a$ for which
$f(a)=0$ hence

$3*a^6+1=0=>a^6=-1/3$

which is impossible because the first part is always positive and the second is negative.

What are the real zeros of f(x) = 3x^6 + 1f(x) = 3x^6 + 1?