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

The solutions to the equation x^4-4x^3+x^2+6x-4=0 are x=1,x=1+sqrt(5),x=1-sqrt(5)

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

The zeros of x^4-4x^3+x^2+6x-4=0 are x=1,x=1+sqrt(5),x=1-sqrt(5)

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

x = 1, x = 1 + 5, x = 1 - 5

Decimal Notation

x = 1, x = 3.23606 \dots, x = - 1.23606 \dots

Solution steps

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

Factor

x^{4} - 4 x^{3} + x^{2} + 6 x - 4 : (x - 1)^{2} (x^{2} - 2 x - 4)

(x - 1)^{2} (x^{2} - 2 x - 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{2} - 2 x - 4 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{2} - 2 x - 4 = 0 : x = 1 + 5, x = 1 - 5

The solutions are

x = 1, x = 1 + 5, x = 1 - 5

d^{4} + 1 = 0

(3 x + 2) (2 x + 2) (x + 1) = 2944

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

5 x^{3} + 3 x^{2} - 7 x + 8 = 0

4 x^{3} - 6 x = 0

What are the solutions to the equation x^4-4x^3+x^2+6x-4=0 ?
The solutions to the equation x^4-4x^3+x^2+6x-4=0 are x=1,x=1+sqrt(5),x=1-sqrt(5)
Find the zeros of x^4-4x^3+x^2+6x-4=0
The zeros of x^4-4x^3+x^2+6x-4=0 are x=1,x=1+sqrt(5),x=1-sqrt(5)