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

All four roots are complex.

Step-by-step explanation:

Given:

First we write as standard form.

Let x² be y

For finding zeros to set the equation 0

Using quadratic formula:

a=5, b=-3 and c=7

Square root of complex number is complex.

Hence, All four roots are complex.

The given polynomial is a four-degree polynomial. The given polynomial has four roots which are all complex.

Given:

The polynomial is

Let . Arrange the polynomial as,

Solve the above quadratic polynomial using the quadratic formula,

So, the value of x will be,

The value of x will be complex number.

Therefore, the given polynomial has four roots which are all complex.

For more details, refer to the link:

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step-by-step explanatio89