How do you solve #(2x ^ { 3} + 3x ) ( x ^ { 2} + 4x + 4) x = 0#?

1 Answer
Jim G.
Jun 23, 2017

#"see explanation"#

Explanation:

#"the equation is in factorised form hence equate each of "#
#"the factors to zero"#

#x=0rArrx=0" is a solution"#

#x^2+4x+4=0to(x+2)^2=0#

#rArrx=-2" multiplicity 2 are solutions"#

#2x^3+3x=0tox(2x^2+3)=0#

#rArrx=0" is a solution"#

#2x^2+3=0tox^2=-3/2#

#rArrx=+-isqrt(3/2)" are complex solutions"#

#color(blue)"the solutions are"#

#x=0to" multiplicity 2"#

#x=-2to" multiplicity 2"#

#x=+-isqrt(3/2)#

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