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

The solutions to the equation 2a^3-3a^2+1=0 are a=1,a=-1/2

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

The zeros of 2a^3-3a^2+1=0 are a=1,a=-1/2

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

a = 1, a = - \frac{1}{2}

Solution steps

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

Factor

2 a^{3} - 3 a^{2} + 1 : (a - 1)^{2} (2 a + 1)

(a - 1)^{2} (2 a + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

a - 1 = 0 or 2 a + 1 = 0

Solve

a - 1 = 0 : a = 1

Solve

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

The solutions are

a = 1, a = - \frac{1}{2}

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

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

2 x^{4} - 5 x^{2} + 36 = x^{4} + 8 x^{2}

5 x^{1} + 10 x^{2} + 15 x^{3} = 50

2 x^{4} = 432 x

What are the solutions to the equation 2a^3-3a^2+1=0 ?
The solutions to the equation 2a^3-3a^2+1=0 are a=1,a=-1/2
Find the zeros of 2a^3-3a^2+1=0
The zeros of 2a^3-3a^2+1=0 are a=1,a=-1/2