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

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

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

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

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roots

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

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

Solution steps

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

The roots are the intercepts with the x-axis

(y = 0)

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

a^{4} + a^{3} + a^{2} + a + 1 = 0

x^{4} - 113 x^{2} + 3136 = 0

x^{4} - 3 x^{3} - 5 x^{2} + 6 x - 8

m^{5} - m = 0

- 9 x^{10} + 10 x^{9} = 0.75

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