What are the solutions to the equation x^4+16x-12=0 ?

The solutions to the equation x^4+16x-12=0 are x=-1+sqrt(3),x=-1-sqrt(3),x=1+sqrt(5)i,x=1-sqrt(5)i

Find the zeros of x^4+16x-12=0

The zeros of x^4+16x-12=0 are x=-1+sqrt(3),x=-1-sqrt(3),x=1+sqrt(5)i,x=1-sqrt(5)i

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x^{4} + 16 x - 12 = 0

x = - 1 + 3, x = - 1 - 3, x = 1 + 5 i, x = 1 - 5 i

Solution steps

x^{4} + 16 x - 12 = 0

Factor

x^{4} + 16 x - 12 : (x^{2} + 2 x - 2) (x^{2} - 2 x + 6)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Solve

x^{2} - 2 x + 6 = 0 : x = 1 + 5 i, x = 1 - 5 i

The solutions are

x = - 1 + 3, x = - 1 - 3, x = 1 + 5 i, x = 1 - 5 i

2 x^{4} + 5 x^{3} - 12 x^{2} = 0

x^{3} - 6 x^{2} - 36 x = - 216

c x^{2} + 2 x = x^{3} - c x

2 t^{3} - 3 t^{2} - 12 t - 42 = 0

4 x^{3} - 24 x^{2} + 32 x = 0

What are the solutions to the equation x^4+16x-12=0 ?
The solutions to the equation x^4+16x-12=0 are x=-1+sqrt(3),x=-1-sqrt(3),x=1+sqrt(5)i,x=1-sqrt(5)i
Find the zeros of x^4+16x-12=0
The zeros of x^4+16x-12=0 are x=-1+sqrt(3),x=-1-sqrt(3),x=1+sqrt(5)i,x=1-sqrt(5)i