Solve -x^3+2x^2+9x+22

Question

I need to find the real and complex solutions.

Answer 1

The cubic polynomial is -x ³ + 2x ² + 9x + 22

f (x ) = -x ³ + 2x ² + 9x + 22

Graph

The points where it crosses the x  axis  will give solutions to the polynimial function .

The graph crosses the x  - axis at a point that would suggest a factor.

It crosses the x  - axis at one point hence there are one real root.

x  = 4.8167

Use synthatic division to detrmine if the given value of x  is a root of the polynomial.

Since f (4.8167)   =   0,   x   =   4.8167 is a zero.

The depressed polynomial is 

Since the depressed polynomial of this zero, , is quadratic,

use the Quadratic Formula to find the roots of the related quadratic equation

 

The cubic polynomial 

Real solution is 

And complex solution is .