What are the solutions to the equation x^4+4x^3-5x^2-16x+4=0 ?

The solutions to the equation x^4+4x^3-5x^2-16x+4=0 are x=-2,x=2,x=-2+sqrt(5),x=-2-sqrt(5)

Find the zeros of x^4+4x^3-5x^2-16x+4=0

The zeros of x^4+4x^3-5x^2-16x+4=0 are x=-2,x=2,x=-2+sqrt(5),x=-2-sqrt(5)

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x^{4} + 4 x^{3} - 5 x^{2} - 16 x + 4 = 0

x = - 2, x = 2, x = - 2 + 5, x = - 2 - 5

Decimal

x = - 2, x = 2, x = 0.23606 \dots, x = - 4.23606 \dots

Solution steps

x^{4} + 4 x^{3} - 5 x^{2} - 16 x + 4 = 0

Factor

x^{4} + 4 x^{3} - 5 x^{2} - 16 x + 4 : (x + 2) (x - 2) (x^{2} + 4 x - 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 2 = 0 : x = - 2

Solve

x - 2 = 0 : x = 2

Solve

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

The solutions are

x = - 2, x = 2, x = - 2 + 5, x = - 2 - 5

3 x^{5} + x^{4} - 9 x^{3} - 9 x^{2} - 2 x = 0

x + x^{3} = 4

x^{3} + 125 = 0

x^{4} + 13 x^{2} + 40 = 0

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

What are the solutions to the equation x^4+4x^3-5x^2-16x+4=0 ?
The solutions to the equation x^4+4x^3-5x^2-16x+4=0 are x=-2,x=2,x=-2+sqrt(5),x=-2-sqrt(5)
Find the zeros of x^4+4x^3-5x^2-16x+4=0
The zeros of x^4+4x^3-5x^2-16x+4=0 are x=-2,x=2,x=-2+sqrt(5),x=-2-sqrt(5)