Question

Find all actual roots of this equation?

2x^4-3x^3-17x^2+41x-21

Answer 1

Step 1:

The polynomial is .

It is possible to find the roots of this polynomial using graphically.

Graph :

Graph the polynomial :

Observe the graph :

Real roots are x-intercept of the graph of .

Graphically the roots of the polynomial are .

Step 2:

To find the remaining two roots, reduce the polynomial using synthetic division method.

Make a table for synthetic division method :

The reduced polynomial is .

Again make a table for synthetic division method :

The reduced polynomial is .

Step 3:

The roots of the quadratic equation are .

The quadratic equation is .

The roots of the quadratic equation are .

Solution :

The roots of the polynomial are , .