Question

How many real roots will be there for the equation $x^{10}+x^8+x^6+x^4+x^2+8=0?$ ___

Answer 1

$f\left(x\right)=x^{10}+x^8+x^6+x^4+x^2+8=0$
No. of sign changes = 0.
Hence, the number of positive real roots =0.
Now, $f\left(x\right)=x^{10}+x^8+x^6+x^4+x^2+8=0$
No. of sign changes = 0.
Hence, the number of negative real roots =0.
The number of real roots for the given equation is 0.