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

1 Answer
Jim G.
Mar 17, 2018

#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"#

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