What are the solutions to the equation x^5-3x^4-15x^3+45x^2-16x+48=0 ?

The solutions to the equation x^5-3x^4-15x^3+45x^2-16x+48=0 are x=3,x=i,x=-i,x=-4,x=4

Find the zeros of x^5-3x^4-15x^3+45x^2-16x+48=0

The zeros of x^5-3x^4-15x^3+45x^2-16x+48=0 are x=3,x=i,x=-i,x=-4,x=4

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x^{5} - 3 x^{4} - 15 x^{3} + 45 x^{2} - 16 x + 48 = 0

x = 3, x = i, x = - i, x = - 4, x = 4

Solution steps

x^{5} - 3 x^{4} - 15 x^{3} + 45 x^{2} - 16 x + 48 = 0

Factor

x^{5} - 3 x^{4} - 15 x^{3} + 45 x^{2} - 16 x + 48 : (x - 3) (x^{2} + 1) (x + 4) (x - 4)

(x - 3) (x^{2} + 1) (x + 4) (x - 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or x^{2} + 1 = 0 or x + 4 = 0 or x - 4 = 0

Solve

x - 3 = 0 : x = 3

Solve

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

Solve

x + 4 = 0 : x = - 4

Solve

x - 4 = 0 : x = 4

The solutions are

x = 3, x = i, x = - i, x = - 4, x = 4

x^{4} - x^{2} = 3 x^{3} - 3 x

m^{4} - 2 m^{2} - 8 = 0

(x + 3)^{4} + 2 (x + 3)^{2} - 8 = 0

x^{3} + 3 x^{2} - 112 = 0

x^{4} - \frac{6}{7} x^{2} + \frac{3}{35} = 0

What are the solutions to the equation x^5-3x^4-15x^3+45x^2-16x+48=0 ?
The solutions to the equation x^5-3x^4-15x^3+45x^2-16x+48=0 are x=3,x=i,x=-i,x=-4,x=4
Find the zeros of x^5-3x^4-15x^3+45x^2-16x+48=0
The zeros of x^5-3x^4-15x^3+45x^2-16x+48=0 are x=3,x=i,x=-i,x=-4,x=4