What are the solutions to the equation x^4-128*x^2-8192*x-61440=0 ?

The solutions to the equation x^4-128*x^2-8192*x-61440=0 are x=-8,x=24,x=-8+16i,x=-8-16i

Find the zeros of x^4-128*x^2-8192*x-61440=0

The zeros of x^4-128*x^2-8192*x-61440=0 are x=-8,x=24,x=-8+16i,x=-8-16i

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x^{4} - 128 \cdot x^{2} - 8192 \cdot x - 61440 = 0

x = - 8, x = 24, x = - 8 + 16 i, x = - 8 - 16 i

Solution steps

x^{4} - 128 x^{2} - 8192 x - 61440 = 0

Factor

x^{4} - 128 x^{2} - 8192 x - 61440 : (x + 8) (x - 24) (x^{2} + 16 x + 320)

(x + 8) (x - 24) (x^{2} + 16 x + 320) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 8 = 0 or x - 24 = 0 or x^{2} + 16 x + 320 = 0

Solve

x + 8 = 0 : x = - 8

Solve

x - 24 = 0 : x = 24

Solve

x^{2} + 16 x + 320 = 0 : x = - 8 + 16 i, x = - 8 - 16 i

The solutions are

x = - 8, x = 24, x = - 8 + 16 i, x = - 8 - 16 i

6 x^{3} - 5 x - 1 = 0

x^{4} + 4 x^{2} + 1 = 0

x^{4} - 5 x^{3} + 6 x^{2} + 4 x - 8 = 0

15 x^{4} + 14 x^{3} - 22 x^{2} - 5 x + 6

8 x^{4} + 10 x^{2} - 12 = 0

What are the solutions to the equation x^4-128*x^2-8192*x-61440=0 ?
The solutions to the equation x^4-128*x^2-8192*x-61440=0 are x=-8,x=24,x=-8+16i,x=-8-16i
Find the zeros of x^4-128*x^2-8192*x-61440=0
The zeros of x^4-128*x^2-8192*x-61440=0 are x=-8,x=24,x=-8+16i,x=-8-16i