What are the solutions to the equation x^4-7x^3+10x^2-2x+4=0 ?

The solutions to the equation x^4-7x^3+10x^2-2x+4=0 are x=2,x\approx 5.07757…

Find the zeros of x^4-7x^3+10x^2-2x+4=0

The zeros of x^4-7x^3+10x^2-2x+4=0 are x=2,x\approx 5.07757…

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x^{4} - 7 x^{3} + 10 x^{2} - 2 x + 4 = 0

x = 2, x \approx 5.07757 \dots

Solution steps

x^{4} - 7 x^{3} + 10 x^{2} - 2 x + 4 = 0

Factor

x^{4} - 7 x^{3} + 10 x^{2} - 2 x + 4 : (x - 2) (x^{3} - 5 x^{2} - 2)

(x - 2) (x^{3} - 5 x^{2} - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 2 = 0 : x = 2

Solve

x^{3} - 5 x^{2} - 2 = 0 : x \approx 5.07757 \dots

The solutions are

x = 2, x \approx 5.07757 \dots

k^{3} = - 1

(x^{2} - 9) (x^{3} - 8) = 0

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

15 x^{4} - 445 x^{2} + 8000 = 0

x^{3} + x - 1 = 1

What are the solutions to the equation x^4-7x^3+10x^2-2x+4=0 ?
The solutions to the equation x^4-7x^3+10x^2-2x+4=0 are x=2,x\approx 5.07757…
Find the zeros of x^4-7x^3+10x^2-2x+4=0
The zeros of x^4-7x^3+10x^2-2x+4=0 are x=2,x\approx 5.07757…