Question

please explain why the function f(x)=2x^6+x^4+4x^2+3 can have no real zeros and hence no rational zeros.

Answer 1

for all negative numbers when the power is applied the answer will be positive and not cancel out the constant 3. because there is a constant, 0 will not work. and for all positive numbers the same issue occurs as with negative numbers.

so, for all real numbers there is no rational zero.

Answer 2

ie f(x) is always positive for every value of x