What are the solutions to the equation 7x^4=56x ?

The solutions to the equation 7x^4=56x are x=0,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i

Find the zeros of 7x^4=56x

The zeros of 7x^4=56x are x=0,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i

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7 x^{4} = 56 x

x = 0, x = 2, x = - 1 + 3 i, x = - 1 - 3 i

Solution steps

7 x^{4} = 56 x

Move

56 x

to the left side

7 x^{4} - 56 x = 0

Factor

7 x^{4} - 56 x : 7 x (x - 2) (x^{2} + 2 x + 4)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

x^{2} + 2 x + 4 = 0 : x = - 1 + 3 i, x = - 1 - 3 i

The solutions are

x = 0, x = 2, x = - 1 + 3 i, x = - 1 - 3 i

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

x^{4} + 3 x^{2} - 28 = 0

x^{3} + 4 x^{2} = 0

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

512 x^{3} = 8

What are the solutions to the equation 7x^4=56x ?
The solutions to the equation 7x^4=56x are x=0,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i
Find the zeros of 7x^4=56x
The zeros of 7x^4=56x are x=0,x=2,x=-1+sqrt(3)i,x=-1-sqrt(3)i