What are the solutions to the equation x^4+2x^3+22x^2+50x-75=0 ?

The solutions to the equation x^4+2x^3+22x^2+50x-75=0 are x=1,x=-3,x=5i,x=-5i

Find the zeros of x^4+2x^3+22x^2+50x-75=0

The zeros of x^4+2x^3+22x^2+50x-75=0 are x=1,x=-3,x=5i,x=-5i

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x^{4} + 2 x^{3} + 22 x^{2} + 50 x - 75 = 0

x = 1, x = - 3, x = 5 i, x = - 5 i

Solution steps

x^{4} + 2 x^{3} + 22 x^{2} + 50 x - 75 = 0

Factor

x^{4} + 2 x^{3} + 22 x^{2} + 50 x - 75 : (x - 1) (x + 3) (x^{2} + 25)

(x - 1) (x + 3) (x^{2} + 25) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x + 3 = 0 or x^{2} + 25 = 0

Solve

x - 1 = 0 : x = 1

Solve

x + 3 = 0 : x = - 3

Solve

x^{2} + 25 = 0 : x = 5 i, x = - 5 i

The solutions are

x = 1, x = - 3, x = 5 i, x = - 5 i

r^{4} + 14 r^{2} - 14 = 0

x^{3} - 3 x^{2} - 25 x + 75

x^{3} - 8 x + 5 = 0

n^{3} - n = 9 n^{2} - 9

x^{3} - 6 x^{2} + 5 x - 1 = 0

What are the solutions to the equation x^4+2x^3+22x^2+50x-75=0 ?
The solutions to the equation x^4+2x^3+22x^2+50x-75=0 are x=1,x=-3,x=5i,x=-5i
Find the zeros of x^4+2x^3+22x^2+50x-75=0
The zeros of x^4+2x^3+22x^2+50x-75=0 are x=1,x=-3,x=5i,x=-5i