What are the solutions to the equation x^4+2x^3-26x^2-50x+25=0 ?

The solutions to the equation x^4+2x^3-26x^2-50x+25=0 are x=-5,x=5,x=-1+sqrt(2),x=-1-sqrt(2)

Find the zeros of x^4+2x^3-26x^2-50x+25=0

The zeros of x^4+2x^3-26x^2-50x+25=0 are x=-5,x=5,x=-1+sqrt(2),x=-1-sqrt(2)

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x^{4} + 2 x^{3} - 26 x^{2} - 50 x + 25 = 0

x = - 5, x = 5, x = - 1 + 2, x = - 1 - 2

Decimal Notation

x = - 5, x = 5, x = 0.41421 \dots, x = - 2.41421 \dots

Solution steps

x^{4} + 2 x^{3} - 26 x^{2} - 50 x + 25 = 0

Factor

x^{4} + 2 x^{3} - 26 x^{2} - 50 x + 25 : (x + 5) (x - 5) (x^{2} + 2 x - 1)

(x + 5) (x - 5) (x^{2} + 2 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 5 = 0 or x - 5 = 0 or x^{2} + 2 x - 1 = 0

Solve

x + 5 = 0 : x = - 5

Solve

x - 5 = 0 : x = 5

Solve

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

The solutions are

x = - 5, x = 5, x = - 1 + 2, x = - 1 - 2

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

x, y = x^{4}

x^{4} + 4 x^{2} - 12 = 0

x^{3} + 7 x^{2} - x - 7 = 0

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

What are the solutions to the equation x^4+2x^3-26x^2-50x+25=0 ?
The solutions to the equation x^4+2x^3-26x^2-50x+25=0 are x=-5,x=5,x=-1+sqrt(2),x=-1-sqrt(2)
Find the zeros of x^4+2x^3-26x^2-50x+25=0
The zeros of x^4+2x^3-26x^2-50x+25=0 are x=-5,x=5,x=-1+sqrt(2),x=-1-sqrt(2)