What are the solutions to the equation x^3-ax^2=0 ?

The solutions to the equation x^3-ax^2=0 are x=0,x=a

Find the zeros of x^3-ax^2=0

The zeros of x^3-ax^2=0 are x=0,x=a

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x^{3} - a x^{2} = 0

x = 0, x = a

Solution steps

x^{3} - a x^{2} = 0

Factor

x^{3} - a x^{2} : x^{2} (x - a)

x^{2} (x - a) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - a = 0

Solve

x - a = 0 : x = a

The solutions are

x = 0, x = a

4 x^{3} - 16 x^{2} + 16 x = 0

0 = 2 x^{3} - x^{2} - 8 x + 4

2 x^{3} + 2 x = 0

- x^{3} + 7 x^{2} - 2 x - 40 = 0

x^{4} = 5 x^{2} - 4

What are the solutions to the equation x^3-ax^2=0 ?
The solutions to the equation x^3-ax^2=0 are x=0,x=a
Find the zeros of x^3-ax^2=0
The zeros of x^3-ax^2=0 are x=0,x=a