What are the solutions to the equation 4x^3-12x^2-9x-1=0 ?

The solutions to the equation 4x^3-12x^2-9x-1=0 are x=-1/2 ,x=(7+sqrt(57))/4 ,x=(7-sqrt(57))/4

Find the zeros of 4x^3-12x^2-9x-1=0

The zeros of 4x^3-12x^2-9x-1=0 are x=-1/2 ,x=(7+sqrt(57))/4 ,x=(7-sqrt(57))/4

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4 x^{3} - 12 x^{2} - 9 x - 1 = 0

x = - \frac{1}{2}, x = \frac{7 + 57}{4}, x = \frac{7 - 57}{4}

Decimal

x = - 0.5, x = 3.63745 \dots, x = - 0.13745 \dots

Solution steps

4 x^{3} - 12 x^{2} - 9 x - 1 = 0

Factor

4 x^{3} - 12 x^{2} - 9 x - 1 : (2 x + 1) (2 x^{2} - 7 x - 1)

(2 x + 1) (2 x^{2} - 7 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 x + 1 = 0 or 2 x^{2} - 7 x - 1 = 0

Solve

2 x + 1 = 0 : x = - \frac{1}{2}

Solve

2 x^{2} - 7 x - 1 = 0 : x = \frac{7 + 57}{4}, x = \frac{7 - 57}{4}

The solutions are

x = - \frac{1}{2}, x = \frac{7 + 57}{4}, x = \frac{7 - 57}{4}

2 x^{3} + 3 x^{2} - 12 x + 1 = 0

x^{3} - 2 x^{2} - 25 x + 50 = 0

H^{3} - 0.479 H^{2} + 0.01 = 0

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

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

What are the solutions to the equation 4x^3-12x^2-9x-1=0 ?
The solutions to the equation 4x^3-12x^2-9x-1=0 are x=-1/2 ,x=(7+sqrt(57))/4 ,x=(7-sqrt(57))/4
Find the zeros of 4x^3-12x^2-9x-1=0
The zeros of 4x^3-12x^2-9x-1=0 are x=-1/2 ,x=(7+sqrt(57))/4 ,x=(7-sqrt(57))/4