What are the solutions to the equation x^2(x-5)+5-x=0 ?

The solutions to the equation x^2(x-5)+5-x=0 are x=5,x=-1,x=1

Find the zeros of x^2(x-5)+5-x=0

The zeros of x^2(x-5)+5-x=0 are x=5,x=-1,x=1

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x^{2} (x - 5) + 5 - x = 0

x = 5, x = - 1, x = 1

Solution steps

x^{2} (x - 5) + 5 - x = 0

Expand

x^{2} (x - 5) + 5 - x : x^{3} - 5 x^{2} + 5 - x

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

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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

Factor

x^{3} - 5 x^{2} - x + 5 : (x - 5) (x + 1) (x - 1)

(x - 5) (x + 1) (x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 5 = 0 or x + 1 = 0 or x - 1 = 0

Solve

x - 5 = 0 : x = 5

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

The solutions are

x = 5, x = - 1, x = 1

x^{4} + x^{3} - 6 x^{2} + 7 x + 49 = 0

x^{4} - 1 3^{2} + 36 = 0

x^{3} + x^{2} - 26 x + 24 = 0

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

x^{4} - 3 x^{3} + 6 x^{2} + 2 x - 60 = 0

What are the solutions to the equation x^2(x-5)+5-x=0 ?
The solutions to the equation x^2(x-5)+5-x=0 are x=5,x=-1,x=1
Find the zeros of x^2(x-5)+5-x=0
The zeros of x^2(x-5)+5-x=0 are x=5,x=-1,x=1