What are the solutions to the equation x^4+62x^2+128x+65=0 ?

The solutions to the equation x^4+62x^2+128x+65=0 are x=-1,x=1+8i,x=1-8i

Find the zeros of x^4+62x^2+128x+65=0

The zeros of x^4+62x^2+128x+65=0 are x=-1,x=1+8i,x=1-8i

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x^{4} + 62 x^{2} + 128 x + 65 = 0

x = - 1, x = 1 + 8 i, x = 1 - 8 i

Solution steps

x^{4} + 62 x^{2} + 128 x + 65 = 0

Factor

x^{4} + 62 x^{2} + 128 x + 65 : (x + 1)^{2} (x^{2} - 2 x + 65)

(x + 1)^{2} (x^{2} - 2 x + 65) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x^{2} - 2 x + 65 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x^{2} - 2 x + 65 = 0 : x = 1 + 8 i, x = 1 - 8 i

The solutions are

x = - 1, x = 1 + 8 i, x = 1 - 8 i

x^{3} - 11 x^{2} + 26 x - 16 = 0

x^{3} + 4 x^{2} - 5 x - 20 = 0

x^{3} - 3 x^{2} - 13 x + 15

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

x^{3} - 5 x^{2} + 4 x - 20

What are the solutions to the equation x^4+62x^2+128x+65=0 ?
The solutions to the equation x^4+62x^2+128x+65=0 are x=-1,x=1+8i,x=1-8i
Find the zeros of x^4+62x^2+128x+65=0
The zeros of x^4+62x^2+128x+65=0 are x=-1,x=1+8i,x=1-8i