What are the solutions to the equation 3x^4-3x^3=10x^2 ?

The solutions to the equation 3x^4-3x^3=10x^2 are x=0,x=(3+sqrt(129))/6 ,x=(3-sqrt(129))/6

Find the zeros of 3x^4-3x^3=10x^2

The zeros of 3x^4-3x^3=10x^2 are x=0,x=(3+sqrt(129))/6 ,x=(3-sqrt(129))/6

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3 x^{4} - 3 x^{3} = 10 x^{2}

x = 0, x = \frac{3 + 129}{6}, x = \frac{3 - 129}{6}

Solution steps

3 x^{4} - 3 x^{3} = 10 x^{2}

Move

10 x^{2}

to the left side

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

Factor

3 x^{4} - 3 x^{3} - 10 x^{2} : x^{2} (3 x^{2} - 3 x - 10)

x^{2} (3 x^{2} - 3 x - 10) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 3 x^{2} - 3 x - 10 = 0

Solve

3 x^{2} - 3 x - 10 = 0 : x = \frac{3 + 129}{6}, x = \frac{3 - 129}{6}

The solutions are

x = 0, x = \frac{3 + 129}{6}, x = \frac{3 - 129}{6}

x^{3} - 2 x - 8 = 0

a \cdot a^{2} \cdot a^{3} = a^{5}

x^{3} - 6 x^{2} - 7 x - 52 = 0

(3 x - 2) (x - 4) (x + 5) = 0

10 x^{2} - 15 = 3 x (6 x^{2} - 5 x)

What are the solutions to the equation 3x^4-3x^3=10x^2 ?
The solutions to the equation 3x^4-3x^3=10x^2 are x=0,x=(3+sqrt(129))/6 ,x=(3-sqrt(129))/6
Find the zeros of 3x^4-3x^3=10x^2
The zeros of 3x^4-3x^3=10x^2 are x=0,x=(3+sqrt(129))/6 ,x=(3-sqrt(129))/6