How many real roots does this polynomial have?

Algebra Level 2

How many real roots does the polynomial x 8 + x 6 + x 4 + x 2 + 1 x^8+x^6+x^4+x^2+1 have?

8 4 None 2

Thiruvikraman Kandhadai by Thiruvikraman Kandhadai , 51, India

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1 solution

All the terms in this polynomial are always positive (we only have even powers of x). Therefore the value of this polynomial is always positive and can never become zero for any real value of x. Therefore none of the roots are real.

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