What are the solutions to the equation 4x^3-12x^2+2x+6=0 ?

The solutions to the equation 4x^3-12x^2+2x+6=0 are x=1,x=(2+sqrt(10))/2 ,x=(2-sqrt(10))/2

Find the zeros of 4x^3-12x^2+2x+6=0

The zeros of 4x^3-12x^2+2x+6=0 are x=1,x=(2+sqrt(10))/2 ,x=(2-sqrt(10))/2

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4 x^{3} - 12 x^{2} + 2 x + 6 = 0

x = 1, x = \frac{2 + 10}{2}, x = \frac{2 - 10}{2}

Decimal

x = 1, x = 2.58113 \dots, x = - 0.58113 \dots

Solution steps

4 x^{3} - 12 x^{2} + 2 x + 6 = 0

Factor

4 x^{3} - 12 x^{2} + 2 x + 6 : 2 (x - 1) (2 x^{2} - 4 x - 3)

2 (x - 1) (2 x^{2} - 4 x - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

2 x^{2} - 4 x - 3 = 0 : x = \frac{2 + 10}{2}, x = \frac{2 - 10}{2}

The solutions are

x = 1, x = \frac{2 + 10}{2}, x = \frac{2 - 10}{2}

x^{4} - x^{3} - 10 x^{2} - x + 1 = 0

2 x^{3} + 5 x^{2} - 4 x - 3 = 0

4 x^{3} = 36

x^{3} - 10 x^{2} + 28 x - 24 = 0

x^{3} - 3 x^{2} - 5 x + 15 = 0

What are the solutions to the equation 4x^3-12x^2+2x+6=0 ?
The solutions to the equation 4x^3-12x^2+2x+6=0 are x=1,x=(2+sqrt(10))/2 ,x=(2-sqrt(10))/2
Find the zeros of 4x^3-12x^2+2x+6=0
The zeros of 4x^3-12x^2+2x+6=0 are x=1,x=(2+sqrt(10))/2 ,x=(2-sqrt(10))/2