I've been given practice exam question:
x^3 - 3x^2 = 0 are 0 and 3.
How do I show that these two numbers are the roots of the equation? I know that when it follows ax^2 + bx + c = 0, the quadratic formula can be used, but this isn't.
Show that the Roots of the Equation x^3 - 3x^2 = 0 are 0 and 3?
2008-04-25 3:46 pm
回答 (7)
2008-04-25 3:52 pm
✔ 最佳答案
[4]x^3-3x^2=0
x^2(x-3)=0
Therefore,either x^2=0 or x-3=0
If x^2=0,then x=0
If x-3=0,then x=3
So,x=0 or 3
2008-04-25 7:04 pm
x² (x - 3) = 0
x = 0 , x = 3
x = 0 , x = 3
2008-04-25 3:58 pm
=x^3-3x^2
=x^2(x-3)
x^2=0 x-3=0
x=0 x=3
it can be shown as follows
by putting 3 in the given equation
=(3)^3-3*(3)^2
=27-27
=0
hence x^3-3x^2=0
3and 0 are the roots of the equation
=x^2(x-3)
x^2=0 x-3=0
x=0 x=3
it can be shown as follows
by putting 3 in the given equation
=(3)^3-3*(3)^2
=27-27
=0
hence x^3-3x^2=0
3and 0 are the roots of the equation
2008-04-25 3:52 pm
x^3 - 3x^2 = 0 ( Take out common factor x^2 )
x^2 ( x - 3 ) = 0
x^2 = 0 OR x-3 = 0
x = 0 OR 3
x^2 ( x - 3 ) = 0
x^2 = 0 OR x-3 = 0
x = 0 OR 3
2008-04-25 3:51 pm
x^3 - 3x^2 = 0
x^2(x - 3) = 0
x^2 = 0
x = â0
x = 0
x - 3 = 0
x = 3
â´ x = 0 , 3
x^2(x - 3) = 0
x^2 = 0
x = â0
x = 0
x - 3 = 0
x = 3
â´ x = 0 , 3
2008-04-25 3:51 pm
'a is a root of f' means f(a) = 0
So by inspection for f(x) = x³ - 3 x²
f(0) = f(3) = 0
So by inspection for f(x) = x³ - 3 x²
f(0) = f(3) = 0
2008-04-25 3:50 pm
x^3 - 3x^2 = 0
x(x^3 - 3) = 0
x = 0 or x^2 - 3 = 0
x =0 or x^2 = 3
x = 0 or x = sqrt3 or -sqrt3.
x = 0, sqrt3, -sqrt3
0 is one of the roots, but 3 is not. The roots are 0, sqrt3, and
-sqrt3.
x(x^3 - 3) = 0
x = 0 or x^2 - 3 = 0
x =0 or x^2 = 3
x = 0 or x = sqrt3 or -sqrt3.
x = 0, sqrt3, -sqrt3
0 is one of the roots, but 3 is not. The roots are 0, sqrt3, and
-sqrt3.
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