What are the solutions to the equation 6p+2=p^2+3p^3 ?

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

Find the zeros of 6p+2=p^2+3p^3

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

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6 p + 2 = p^{2} + 3 p^{3}

p = - \frac{1}{3}, p = - 2, p = 2

Decimal Notation

p = - 0.33333 \dots, p = - 1.41421 \dots, p = 1.41421 \dots

Solution steps

6 p + 2 = p^{2} + 3 p^{3}

Switch sides

p^{2} + 3 p^{3} = 6 p + 2

Move

2

to the left side

p^{2} + 3 p^{3} - 2 = 6 p

Move

6 p

to the left side

p^{2} + 3 p^{3} - 2 - 6 p = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

3 p^{3} + p^{2} - 6 p - 2 = 0

Factor

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

(3 p + 1) (p + 2) (p - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

3 p + 1 = 0 or p + 2 = 0 or p - 2 = 0

Solve

3 p + 1 = 0 : p = - \frac{1}{3}

Solve

p + 2 = 0 : p = - 2

Solve

p - 2 = 0 : p = 2

The solutions are

p = - \frac{1}{3}, p = - 2, p = 2

n, A = 2 r h + 2 s n^{3}

x^{3} - 15 x^{2} + 27 x - 13 = 0

x^{3} - 7 x^{2} + 19 x - 13 = 0

5 x^{4} + 8 x^{3} + 3 x^{2} = 0

x^{125} = 3

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