Solve each equation. What is the number and types of roots? #x^3 -6x^2+7x=0#

1 Answer
Daniel L.
Mar 20, 2018

See explanation.

Explanation:

#x^3-6x^2+7x=0#

#x(x^2-6x+7)=0#

#x=0 vv x^2-6x+7=0#

#x^2-6x+7=0#

#Delta=(-6)^2-4*1*7#

#Delta=36-28=8#

#sqrt(Delta)=sqrt(8)=2sqrt(2)#

#x_1=(6-2sqrt(2))/2=3-sqrt(2)#

#x_2=(6+2sqrt(2))/2=3+sqrt(2)#

Answer: The equation has 3 real roots:

#x_1=0#, #x_2=3-sqrt(2)#, #x_3=3+sqrt(2)#

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