What are the solutions to the equation -x^3+14x^2-42x=0 ?

The solutions to the equation -x^3+14x^2-42x=0 are x=0,x=7+sqrt(7),x=7-sqrt(7)

Find the zeros of -x^3+14x^2-42x=0

The zeros of -x^3+14x^2-42x=0 are x=0,x=7+sqrt(7),x=7-sqrt(7)

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- x^{3} + 14 x^{2} - 42 x = 0

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

Decimal

x = 0, x = 9.64575 \dots, x = 4.35424 \dots

Solution steps

- x^{3} + 14 x^{2} - 42 x = 0

Factor

- x^{3} + 14 x^{2} - 42 x : - x (x^{2} - 14 x + 42)

- x (x^{2} - 14 x + 42) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{2} - 14 x + 42 = 0

Solve

x^{2} - 14 x + 42 = 0 : x = 7 + 7, x = 7 - 7

The solutions are

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

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

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

z^{3} - 0.87 z^{2} + 1.74 z - 0.24 = 0

2 c^{4} - 6 c^{3} = 12 c^{2} - 36 c

x^{4} - 6 x^{3} + 17 x^{2} - 24 x + 52 = 0

What are the solutions to the equation -x^3+14x^2-42x=0 ?
The solutions to the equation -x^3+14x^2-42x=0 are x=0,x=7+sqrt(7),x=7-sqrt(7)
Find the zeros of -x^3+14x^2-42x=0
The zeros of -x^3+14x^2-42x=0 are x=0,x=7+sqrt(7),x=7-sqrt(7)