What are the solutions to the equation 4x^3+2x^2-3x-1=0 ?

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

Find the zeros of 4x^3+2x^2-3x-1=0

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

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

x = - 1, x = \frac{1 + 5}{4}, x = \frac{1 - 5}{4}

Decimal Notation

x = - 1, x = 0.80901 \dots, x = - 0.30901 \dots

Solution steps

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

Factor

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

(x + 1) (4 x^{2} - 2 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or 4 x^{2} - 2 x - 1 = 0

Solve

x + 1 = 0 : x = - 1

Solve

4 x^{2} - 2 x - 1 = 0 : x = \frac{1 + 5}{4}, x = \frac{1 - 5}{4}

The solutions are

x = - 1, x = \frac{1 + 5}{4}, x = \frac{1 - 5}{4}

x^{3} + 12 x + 16 = 0

x^{2} + x^{8} = 1565498

x, x^{4} - x^{2} - r = 0

x^{3} - 10 x^{2} + 25 x = 0

x^{3} - 12 x^{2} + 27 x = 0

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