What are the solutions to the equation x^4-2x^3-6x^2=0 ?

The solutions to the equation x^4-2x^3-6x^2=0 are x=0,x=1+sqrt(7),x=1-sqrt(7)

Find the zeros of x^4-2x^3-6x^2=0

The zeros of x^4-2x^3-6x^2=0 are x=0,x=1+sqrt(7),x=1-sqrt(7)

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x^{4} - 2 x^{3} - 6 x^{2} = 0

x = 0, x = 1 + 7, x = 1 - 7

Decimal Notation

x = 0, x = 3.64575 \dots, x = - 1.64575 \dots

Solution steps

x^{4} - 2 x^{3} - 6 x^{2} = 0

Factor

x^{4} - 2 x^{3} - 6 x^{2} : x^{2} (x^{2} - 2 x - 6)

x^{2} (x^{2} - 2 x - 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{2} - 2 x - 6 = 0

Solve

x^{2} - 2 x - 6 = 0 : x = 1 + 7, x = 1 - 7

The solutions are

x = 0, x = 1 + 7, x = 1 - 7

1.576 = (1 + x)^{3}

420 = 130 x^{3} + 30

0 = - x^{3} + 4 \cdot x

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

x^{3} + 4 x^{2} - 20 x = 80

What are the solutions to the equation x^4-2x^3-6x^2=0 ?
The solutions to the equation x^4-2x^3-6x^2=0 are x=0,x=1+sqrt(7),x=1-sqrt(7)
Find the zeros of x^4-2x^3-6x^2=0
The zeros of x^4-2x^3-6x^2=0 are x=0,x=1+sqrt(7),x=1-sqrt(7)