How do I solve this?
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The first thing that you want to do when solving these, is to factor out as much as you can. Basically, everything that these two numbers have in common, factor out. In this case, the two numbers have an "x²" in common. When you take out the x², you get...
x² (x - 6) = 0
This is because x * x² = x^3 and 6 * x² = 6x²
Because these two factors are multiplied together, if one of them is 0, it doesn't matter what the other is, because anything multiplied by 0 will equal 0. Therefore, we have to solve for when each of the factors is 0.
x² = 0
x = 0/x
x = 0
x - 6 = 0
x - 6 + 6 = 0 + 6
x = 6
x² (x - 6) = 0
This is because x * x² = x^3 and 6 * x² = 6x²
Because these two factors are multiplied together, if one of them is 0, it doesn't matter what the other is, because anything multiplied by 0 will equal 0. Therefore, we have to solve for when each of the factors is 0.
x² = 0
x = 0/x
x = 0
x - 6 = 0
x - 6 + 6 = 0 + 6
x = 6
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its
x^2 (x - 6) = 0
ie
either x = 6 or x^2 = 0
ie
x = 0 or x = 6
Thus
Roots of the given cubic equation are
1 , 0 , 0
x^2 (x - 6) = 0
ie
either x = 6 or x^2 = 0
ie
x = 0 or x = 6
Thus
Roots of the given cubic equation are
1 , 0 , 0
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x ² ( x - 6 ) = 0
x = 0 , x = 6
x = 0 , x = 6