Question

f(x)=5x^2+x^4

Answer 1

even odd or neithr

Answer 2

it is even because the exponents are even and any polynomial with all even exponents is even

Answer 3

if even one exponent is odd, then it is not even
but the exponents here are 2 and 4, that makes it even

Answer 4

\(\large\color{black}{f(x)=5x^2+x^4}\)

\(\large\color{black}{f(x)=x^2(5+x^2)}\)

Answer 5

if you want to find zeros, set f(x)=0, and solve for x.

Answer 6

(you will have 2 imaginary and 2 real solutions)

Answer 7

One test for even functions is f(x)=f(-x).
So try to evaluate f(-x) and see if it becomes f(x), that shows that it is even.
\(f(-x)=5(-x)^2+(-x)^4=5x^2+x^4=f(x)\)
Since f(x)=f(-x), we conclude that f(x) is even.
Note that this test applies to trig or other functions, and not limited to polynomials.

By the way, equivalent test for odd functions is f(-x)=-f(x)