Question

How do you find the real solutions of the polynomial `9x^3=5x^2+x`?

Answer 1

`x=0,x=5/18+-1/18sqrt61`

Explanation:

`"rearrange into standard form"`

`rArr9x^3-5x^2-x=0larrcolor(blue)"in standard form"`

`rArrx(9x^2-5x-1)=0`

`"equate each factor to zero and solve for x"`

`rArrx=0" or "9x^2-5x-1=0`

`"solve "9x^2-5x-1=0" using the "color(blue)"quadratic formula"`

`"with "a=9,b=-5" and "c=-1`

`x=(5+-sqrt(25+36))/18`

`color(white)(x)=(5+-sqrt61)/18`

`rArrx=5/18+-1/18sqrt61`

`rArrx=0,x=5/18+-1/18sqrt61larrcolor(blue)"real solutions"`