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

The solutions to the equation x^3+4x^2-2x-3=0 are x=1,x=(-5+sqrt(13))/2 ,x=(-5-sqrt(13))/2

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

The zeros of x^3+4x^2-2x-3=0 are x=1,x=(-5+sqrt(13))/2 ,x=(-5-sqrt(13))/2

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

x = 1, x = \frac{- 5 + 13}{2}, x = \frac{- 5 - 13}{2}

Decimal

x = 1, x = - 0.69722 \dots, x = - 4.30277 \dots

Solution steps

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

Factor

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

(x - 1) (x^{2} + 5 x + 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{2} + 5 x + 3 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{2} + 5 x + 3 = 0 : x = \frac{- 5 + 13}{2}, x = \frac{- 5 - 13}{2}

The solutions are

x = 1, x = \frac{- 5 + 13}{2}, x = \frac{- 5 - 13}{2}

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

x^{3} + 2 x = 1

12 x^{3} + 12 x^{2} - 12 x = 0

3 x^{4} + 6 x^{2} + 1 = 0

x^{3} - 10 x - 24 = 0

What are the solutions to the equation x^3+4x^2-2x-3=0 ?
The solutions to the equation x^3+4x^2-2x-3=0 are x=1,x=(-5+sqrt(13))/2 ,x=(-5-sqrt(13))/2
Find the zeros of x^3+4x^2-2x-3=0
The zeros of x^3+4x^2-2x-3=0 are x=1,x=(-5+sqrt(13))/2 ,x=(-5-sqrt(13))/2