What are the solutions to the equation v^2+v^3=12 ?

The solutions to the equation v^2+v^3=12 are v=2,v=-3/2+i(sqrt(15))/2 ,v=-3/2-i(sqrt(15))/2

Find the zeros of v^2+v^3=12

The zeros of v^2+v^3=12 are v=2,v=-3/2+i(sqrt(15))/2 ,v=-3/2-i(sqrt(15))/2

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v^{2} + v^{3} = 12

v = 2, v = - \frac{3}{2} + i \frac{15}{2}, v = - \frac{3}{2} - i \frac{15}{2}

Solution steps

v^{2} + v^{3} = 12

Move

12

to the left side

v^{2} + v^{3} - 12 = 0

Write in the standard form

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

v^{3} + v^{2} - 12 = 0

Factor

v^{3} + v^{2} - 12 : (v - 2) (v^{2} + 3 v + 6)

(v - 2) (v^{2} + 3 v + 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

v - 2 = 0 or v^{2} + 3 v + 6 = 0

Solve

v - 2 = 0 : v = 2

Solve

v^{2} + 3 v + 6 = 0 : v = - \frac{3}{2} + i \frac{15}{2}, v = - \frac{3}{2} - i \frac{15}{2}

The solutions are

v = 2, v = - \frac{3}{2} + i \frac{15}{2}, v = - \frac{3}{2} - i \frac{15}{2}

x^{3} - 11 x^{2} + 18 x = 0

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

x^{3} - 2 x^{2} - 4 x - 8 = 0

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

z^{4} - z^{2} + 1 = 0

What are the solutions to the equation v^2+v^3=12 ?
The solutions to the equation v^2+v^3=12 are v=2,v=-3/2+i(sqrt(15))/2 ,v=-3/2-i(sqrt(15))/2
Find the zeros of v^2+v^3=12
The zeros of v^2+v^3=12 are v=2,v=-3/2+i(sqrt(15))/2 ,v=-3/2-i(sqrt(15))/2