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# find all real number solutions: x^3-3x^2+2x=0

i think you have to factor it first then find the solution(s). if you could explain this to me i would be so grateful!

### 2 Answers by Expert Tutors

Roman C. | Masters of Education Graduate with Mathematics ExpertiseMasters of Education Graduate with Mathe...
4.9 4.9 (349 lesson ratings) (349)
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Although all cubic polynomials can be solved using radicals (Cardano's formula), in most middle and high school classes, all cubics that the teachers and textbooks ask you to solve have rational roots.

In this case, can you see that we can factor out x? this gives x(x2-3x+2).

Also, recall how you factor quadratics using FOIL. In this case, the form is x2-3x+2 = (x - __)(x - __).

We want the sum of the blanks to be 3 and the product to be 2. The only choice would be 1 and 2 (1+2=3 and 1*2 = 2).

So we have x3 - 3x2 + 2x = x(x-1)(x-2) = 0. I assume you can now figure out the roots.

Ritu J. | A truly experienced tutor for Math !!A truly experienced tutor for Math !!
5.0 5.0 (36 lesson ratings) (36)
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the equation is

x3 -3x2 +2x= 0

taking x common on left hand side

x (x2 -3x+2) = 0

x (x-2) (x-1) = 0

This is true for x= 0 or 2 or 1

Hence there are 3 real number solutions