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

The solutions to the equation x^4+3x^3-7x^2+x+2=0 are x=1,x=(-5+sqrt(17))/2 ,x=(-5-sqrt(17))/2

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

The zeros of x^4+3x^3-7x^2+x+2=0 are x=1,x=(-5+sqrt(17))/2 ,x=(-5-sqrt(17))/2

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

x = 1, x = \frac{- 5 + 17}{2}, x = \frac{- 5 - 17}{2}

Decimal Notation

x = 1, x = - 0.43844 \dots, x = - 4.56155 \dots

Solution steps

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

Factor

x^{4} + 3 x^{3} - 7 x^{2} + x + 2 : (x - 1)^{2} (x^{2} + 5 x + 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

x^{2} + 5 x + 2 = 0 : x = \frac{- 5 + 17}{2}, x = \frac{- 5 - 17}{2}

The solutions are

x = 1, x = \frac{- 5 + 17}{2}, x = \frac{- 5 - 17}{2}

p^{3} + 2 p - 27 = 2 p

x^{2} + x + 1 = x^{3} + x^{2} + 1

x^{4} + 4 x^{2} - 5 = 0

6 x = (- 2 x)^{3}

10 x - 8 x^{2} - 2 x^{3} = 0

What are the solutions to the equation x^4+3x^3-7x^2+x+2=0 ?
The solutions to the equation x^4+3x^3-7x^2+x+2=0 are x=1,x=(-5+sqrt(17))/2 ,x=(-5-sqrt(17))/2
Find the zeros of x^4+3x^3-7x^2+x+2=0
The zeros of x^4+3x^3-7x^2+x+2=0 are x=1,x=(-5+sqrt(17))/2 ,x=(-5-sqrt(17))/2