Question

How many roots, real or complex, does the polynomial $7+5{\mathrm{x}}^4-3{\mathrm{x}}^2$ have in all?

Answer 1

Compute the number of roots:

Degree of polynomial: Highest power of the variable in a polynomial.

Degree of $7+5{\mathrm{x}}^4-3{\mathrm{x}}^2$ is $4$ .

As, a polynomial can have maximum $n$ roots which can be real or complex, where $n$ is the degree of polynomial.

So, $7+5{\mathrm{x}}^4-3{\mathrm{x}}^2$ has $4$ roots.

Hence, given polynomial has $4$ roots.