SOLUTION: find all solutions of the equation algebraically 9x^4 - 24x^3 + 16x^2 =0

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Question 180700: find all solutions of the equation algebraically
9x^4 - 24x^3 + 16x^2 =0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

9x%5E4-24x%5E3%2B16x%5E2=0 Start with the given equation


x%5E2%289x%5E2-24x%2B16%29=0 Factor out the GCF x%5E2


x%5E2%283x-4%29%283x-4%29=0 Factor the inner expression by use of the difference of squares formula.


Now set each factor equal to zero:

x%5E2=0, 3x-4=0 or 3x-4=0


x=0, x=0, x=4%2F3 or x=4%2F3 Now solve for x in each case


Since we have repeating answers, our real answers are x=0 or x=4%2F3


So the solutions are x=0 or x=4%2F3