What are the solutions to the equation x^3-6x^2+x+28=0 ?

The solutions to the equation x^3-6x^2+x+28=0 are x=4,x=1+2sqrt(2),x=1-2sqrt(2)

Find the zeros of x^3-6x^2+x+28=0

The zeros of x^3-6x^2+x+28=0 are x=4,x=1+2sqrt(2),x=1-2sqrt(2)

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x^{3} - 6 x^{2} + x + 28 = 0

x = 4, x = 1 + 22, x = 1 - 22

Decimal Notation

x = 4, x = 3.82842 \dots, x = - 1.82842 \dots

Solution steps

x^{3} - 6 x^{2} + x + 28 = 0

Factor

x^{3} - 6 x^{2} + x + 28 : (x - 4) (x^{2} - 2 x - 7)

(x - 4) (x^{2} - 2 x - 7) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 4 = 0 or x^{2} - 2 x - 7 = 0

Solve

x - 4 = 0 : x = 4

Solve

x^{2} - 2 x - 7 = 0 : x = 1 + 22, x = 1 - 22

The solutions are

x = 4, x = 1 + 22, x = 1 - 22

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

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

x^{3} - 7 x^{2} + 5 x + 25 = 0

x^{3} + 5 x^{2} + 4 x + 20

x, x^{3} = a t^{2}

What are the solutions to the equation x^3-6x^2+x+28=0 ?
The solutions to the equation x^3-6x^2+x+28=0 are x=4,x=1+2sqrt(2),x=1-2sqrt(2)
Find the zeros of x^3-6x^2+x+28=0
The zeros of x^3-6x^2+x+28=0 are x=4,x=1+2sqrt(2),x=1-2sqrt(2)