What are the solutions to the equation x^4+5x^3-16x^2+40x-192=0 ?

The solutions to the equation x^4+5x^3-16x^2+40x-192=0 are x=3,x=-8,x=2sqrt(2)i,x=-2sqrt(2)i

Find the zeros of x^4+5x^3-16x^2+40x-192=0

The zeros of x^4+5x^3-16x^2+40x-192=0 are x=3,x=-8,x=2sqrt(2)i,x=-2sqrt(2)i

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x^{4} + 5 x^{3} - 16 x^{2} + 40 x - 192 = 0

x = 3, x = - 8, x = 22 i, x = - 22 i

Solution steps

x^{4} + 5 x^{3} - 16 x^{2} + 40 x - 192 = 0

Factor

x^{4} + 5 x^{3} - 16 x^{2} + 40 x - 192 : (x - 3) (x + 8) (x^{2} + 8)

(x - 3) (x + 8) (x^{2} + 8) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or x + 8 = 0 or x^{2} + 8 = 0

Solve

x - 3 = 0 : x = 3

Solve

x + 8 = 0 : x = - 8

Solve

x^{2} + 8 = 0 : x = 22 i, x = - 22 i

The solutions are

x = 3, x = - 8, x = 22 i, x = - 22 i

y^{3} - y^{2} - 12 y = 0

2 x^{7} = 3 x^{9}

4 x^{4} = 41 x^{2} - 100

x^{4} - 3 x^{3} + 5 x - 1 = 0

- 4 y^{3} + 34 y^{2} + 36 y - 516 = 0

What are the solutions to the equation x^4+5x^3-16x^2+40x-192=0 ?
The solutions to the equation x^4+5x^3-16x^2+40x-192=0 are x=3,x=-8,x=2sqrt(2)i,x=-2sqrt(2)i
Find the zeros of x^4+5x^3-16x^2+40x-192=0
The zeros of x^4+5x^3-16x^2+40x-192=0 are x=3,x=-8,x=2sqrt(2)i,x=-2sqrt(2)i