What are the solutions to the equation x^4+x^5=2x^3 ?

The solutions to the equation x^4+x^5=2x^3 are x=0,x=1,x=-2

Find the zeros of x^4+x^5=2x^3

The zeros of x^4+x^5=2x^3 are x=0,x=1,x=-2

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x^{4} + x^{5} = 2 x^{3}

x = 0, x = 1, x = - 2

Solution steps

x^{4} + x^{5} = 2 x^{3}

Move

2 x^{3}

to the left side

x^{4} + x^{5} - 2 x^{3} = 0

Factor

x^{4} + x^{5} - 2 x^{3} : x^{3} (x - 1) (x + 2)

x^{3} (x - 1) (x + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 1 = 0 or x + 2 = 0

Solve

x - 1 = 0 : x = 1

Solve

x + 2 = 0 : x = - 2

The solutions are

x = 0, x = 1, x = - 2

3 x^{3} - 75 x = 0

2 x^{3} - 7 x^{2} + 14 x - 5 = 0

(x^{2} - 5 x + 7)^{2} - (x - 2) (x - 3) = 1

- 5 x^{4} - 3 x + 4 = 0

x, y = (x - 2)^{3} - 3

What are the solutions to the equation x^4+x^5=2x^3 ?
The solutions to the equation x^4+x^5=2x^3 are x=0,x=1,x=-2
Find the zeros of x^4+x^5=2x^3
The zeros of x^4+x^5=2x^3 are x=0,x=1,x=-2