What are the solutions to the equation x^4-11x^2-12x+4=0 ?

The solutions to the equation x^4-11x^2-12x+4=0 are x=-2,x=2+sqrt(3),x=2-sqrt(3)

Find the zeros of x^4-11x^2-12x+4=0

The zeros of x^4-11x^2-12x+4=0 are x=-2,x=2+sqrt(3),x=2-sqrt(3)

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x^{4} - 11 x^{2} - 12 x + 4 = 0

x = - 2, x = 2 + 3, x = 2 - 3

Decimal Notation

x = - 2, x = 3.73205 \dots, x = 0.26794 \dots

Solution steps

x^{4} - 11 x^{2} - 12 x + 4 = 0

Factor

x^{4} - 11 x^{2} - 12 x + 4 : (x + 2)^{2} (x^{2} - 4 x + 1)

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

Solve

x + 2 = 0 : x = - 2

Solve

x^{2} - 4 x + 1 = 0 : x = 2 + 3, x = 2 - 3

The solutions are

x = - 2, x = 2 + 3, x = 2 - 3

(x - 1) (x^{2} + 6 x + 9) = 5 (x + 3)

x^{3} - 5 x^{2} + 25 x - 125 = 0

8 x^{7} = 9 x^{8}

5 (x - 1) = 5 (x^{5} + 2)

x^{3} + 13 x^{2} + 57 x + 85 = 0

What are the solutions to the equation x^4-11x^2-12x+4=0 ?
The solutions to the equation x^4-11x^2-12x+4=0 are x=-2,x=2+sqrt(3),x=2-sqrt(3)
Find the zeros of x^4-11x^2-12x+4=0
The zeros of x^4-11x^2-12x+4=0 are x=-2,x=2+sqrt(3),x=2-sqrt(3)