What are the solutions to the equation x^4-6x^3-7x^2+54x-18=0 ?

The solutions to the equation x^4-6x^3-7x^2+54x-18=0 are x=-3,x=3,x=3+sqrt(7),x=3-sqrt(7)

Find the zeros of x^4-6x^3-7x^2+54x-18=0

The zeros of x^4-6x^3-7x^2+54x-18=0 are x=-3,x=3,x=3+sqrt(7),x=3-sqrt(7)

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x^{4} - 6 x^{3} - 7 x^{2} + 54 x - 18 = 0

x = - 3, x = 3, x = 3 + 7, x = 3 - 7

Decimal Notation

x = - 3, x = 3, x = 5.64575 \dots, x = 0.35424 \dots

Solution steps

x^{4} - 6 x^{3} - 7 x^{2} + 54 x - 18 = 0

Factor

x^{4} - 6 x^{3} - 7 x^{2} + 54 x - 18 : (x + 3) (x - 3) (x^{2} - 6 x + 2)

(x + 3) (x - 3) (x^{2} - 6 x + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 3 = 0 : x = - 3

Solve

x - 3 = 0 : x = 3

Solve

x^{2} - 6 x + 2 = 0 : x = 3 + 7, x = 3 - 7

The solutions are

x = - 3, x = 3, x = 3 + 7, x = 3 - 7

x^{3} + 19 x^{2} + 90 x + 52 = 0

6 x^{3} + 13 x^{2} + 2 x - 5 = 0

(4 x - 3) (x + 2) (x - 6) = 0

25 x^{2} + 8 x^{3} - 441 = 0

x, 9 x^{3} + 9 y - 27 = 0

What are the solutions to the equation x^4-6x^3-7x^2+54x-18=0 ?
The solutions to the equation x^4-6x^3-7x^2+54x-18=0 are x=-3,x=3,x=3+sqrt(7),x=3-sqrt(7)
Find the zeros of x^4-6x^3-7x^2+54x-18=0
The zeros of x^4-6x^3-7x^2+54x-18=0 are x=-3,x=3,x=3+sqrt(7),x=3-sqrt(7)