What are the solutions to the equation e(x)=(-x+x^2)^2+4x^3 ?

The solutions to the equation e(x)=(-x+x^2)^2+4x^3 are x=0,x\approx 0.82033…

Find the zeros of e(x)=(-x+x^2)^2+4x^3

The zeros of e(x)=(-x+x^2)^2+4x^3 are x=0,x\approx 0.82033…

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e (x) = (- x + x^{2})^{2} + 4 x^{3}

x = 0, x \approx 0.82033 \dots

Solution steps

e (x) = (- x + x^{2})^{2} + 4 x^{3}

Expand

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

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

Switch sides

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

Move

e x

to the left side

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{3} + 2 x^{2} + x - e = 0

Solve

x^{3} + 2 x^{2} + x - e = 0 : x \approx 0.82033 \dots

The solutions are

x = 0, x \approx 0.82033 \dots

3 x^{4} - 24 x^{3} + 48 x^{2} + x - 4 = 0

x, x^{4} + y^{4} = 0

x^{3} - 5 x^{2} + 8 x - 4 = 0

x^{3} + 2 x^{2} - 5 x - 6 = 0

x^{3} + 4 x^{2} - 47 x - 210 = 0

What are the solutions to the equation e(x)=(-x+x^2)^2+4x^3 ?
The solutions to the equation e(x)=(-x+x^2)^2+4x^3 are x=0,x\approx 0.82033…
Find the zeros of e(x)=(-x+x^2)^2+4x^3
The zeros of e(x)=(-x+x^2)^2+4x^3 are x=0,x\approx 0.82033…