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

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

Find the zeros of x^4+4x+3=0

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

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

x = - 1, x = 1 + 2 i, x = 1 - 2 i

Solution steps

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

Factor

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

(x + 1)^{2} (x^{2} - 2 x + 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x^{2} - 2 x + 3 = 0

Solve

x + 1 = 0 : x = - 1

Solve

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

The solutions are

x = - 1, x = 1 + 2 i, x = 1 - 2 i

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

x^{3} + 27

4 x^{3} - 24 x^{2} + 48 x = 0

9 x^{3} + 45 x^{2} + 59 x + 15

64 m = m^{3} - m^{2} + m - 62

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