What are the solutions to the equation 4x^3+12ax^2-16a^2x=0 ?

The solutions to the equation 4x^3+12ax^2-16a^2x=0 are x=0,x=a,x=-4a

Find the zeros of 4x^3+12ax^2-16a^2x=0

The zeros of 4x^3+12ax^2-16a^2x=0 are x=0,x=a,x=-4a

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4 x^{3} + 12 a x^{2} - 16 a^{2} x = 0

x = 0, x = a, x = - 4 a

Solution steps

4 x^{3} + 12 a x^{2} - 16 a^{2} x = 0

Factor

4 x^{3} + 12 a x^{2} - 16 a^{2} x : 4 x (x - a) (x + 4 a)

4 x (x - a) (x + 4 a) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - a = 0 or x + 4 a = 0

Solve

x - a = 0 : x = a

Solve

x + 4 a = 0 : x = - 4 a

The solutions are

x = 0, x = a, x = - 4 a

x^{4} - 2 x^{3} - 8 x + 16 = 0

x^{3} - 8 x = 2 x^{2}

x, y - 1 = x^{3}

x^{3} + 2 = 345

6 x^{3} - x^{2} - 35 x = 0

What are the solutions to the equation 4x^3+12ax^2-16a^2x=0 ?
The solutions to the equation 4x^3+12ax^2-16a^2x=0 are x=0,x=a,x=-4a
Find the zeros of 4x^3+12ax^2-16a^2x=0
The zeros of 4x^3+12ax^2-16a^2x=0 are x=0,x=a,x=-4a