Question

How many complex roots does the polynomial equation have? 3x5−2x+1=0

Answer 1

Answer : The given polynomial equation can have 0,2 or 4 complex roots.

Explanation:-

Given polynomial equation is $3x^5-2x+1=0$ which is a polynomial of degree 5.

We know that the complex roots always occur in pair ,therefore the number of complex roots in any polynomial must be an even number but less than equal  to the degree of polynomial.

Thus, the given polynomial equation has 4 complex roots.

Answer 2

Answer:

The polynomial equation have 4 complex roots.

Step-by-step explanation:

We are given a polynomial equation as:

$3x^5-2x+1=0$

clearly the polynomial equation is a equation of degree 5 hence, the polynomial equation has atmost 5 roots.

Now we find the roots of the equation by it's graph.

we could clearly see that the graph ofthe function passes through the point (-1,0). hence -1 is the root of the polynomial equation, other than this point the graph does not touches or pass through the x-axis.

Hence, the other four roots of the polynomial equation are complex.

Hence, the polynomial equation has 4 complex roots.