What are the solutions to the equation 4b^3-6b^2+1=0 ?

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

Find the zeros of 4b^3-6b^2+1=0

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

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4 b^{3} - 6 b^{2} + 1 = 0

b = \frac{1}{2}, b = \frac{1 + 3}{2}, b = \frac{1 - 3}{2}

Decimal Notation

b = 0.5, b = 1.36602 \dots, b = - 0.36602 \dots

Solution steps

4 b^{3} - 6 b^{2} + 1 = 0

Factor

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

(2 b - 1) (2 b^{2} - 2 b - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 b - 1 = 0 or 2 b^{2} - 2 b - 1 = 0

Solve

2 b - 1 = 0 : b = \frac{1}{2}

Solve

2 b^{2} - 2 b - 1 = 0 : b = \frac{1 + 3}{2}, b = \frac{1 - 3}{2}

The solutions are

b = \frac{1}{2}, b = \frac{1 + 3}{2}, b = \frac{1 - 3}{2}

x^{3} + x - 16 = 0

x^{4} - (5 + 2) \cdot x^{2} + 10 = 0

(x^{2} + x - 6) (x^{2} - 3 x - 4) = 24

x, (3 x + 7)^{5} = 2 y^{3}

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

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