Calculate the number of real roots of x^8−x^5+x^2−x+1=0

sarahkobearab4

sarahkobearab4

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2022-08-19

Calculate the number of real roots of x 8 x 5 + x 2 x + 1 = 0

Answer & Explanation

Rowan Dyer

Rowan Dyer

Beginner2022-08-20Added 14 answers

AM-GM Inequality gives us,
1 2 ( x 8 + x 2 ) x 5
1 2 ( x 2 + 1 ) x
x 8 + x 2 + 1 > 1 2 ( x 8 + x 2 ) + 1 2 ( x 2 + 1 ) x 5 + x
x 8 x 5 + x 2 x + 1 > 0
Hence there cannot exist any real solution for x.

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