What are the solutions to the equation a^3+a^2=36 ?

The solutions to the equation a^3+a^2=36 are a=3,a=-2+2sqrt(2)i,a=-2-2sqrt(2)i

Find the zeros of a^3+a^2=36

The zeros of a^3+a^2=36 are a=3,a=-2+2sqrt(2)i,a=-2-2sqrt(2)i

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a^{3} + a^{2} = 36

a = 3, a = - 2 + 22 i, a = - 2 - 22 i

Solution steps

a^{3} + a^{2} = 36

Move

36

to the left side

a^{3} + a^{2} - 36 = 0

Factor

a^{3} + a^{2} - 36 : (a - 3) (a^{2} + 4 a + 12)

(a - 3) (a^{2} + 4 a + 12) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

a - 3 = 0 or a^{2} + 4 a + 12 = 0

Solve

a - 3 = 0 : a = 3

Solve

a^{2} + 4 a + 12 = 0 : a = - 2 + 22 i, a = - 2 - 22 i

The solutions are

a = 3, a = - 2 + 22 i, a = - 2 - 22 i

- 3 x (2 x - 1) (x + 6)^{2} = 0

45 = 4 y^{3} - 3

x^{4} - 3 x^{3} - 9 x^{2} + 23 x - 12 = 0

x^{3} + 5 x^{2} - 9 x - 45 = 0

x^{3} - 6 x^{2} - 4 x + 24 = 0

What are the solutions to the equation a^3+a^2=36 ?
The solutions to the equation a^3+a^2=36 are a=3,a=-2+2sqrt(2)i,a=-2-2sqrt(2)i
Find the zeros of a^3+a^2=36
The zeros of a^3+a^2=36 are a=3,a=-2+2sqrt(2)i,a=-2-2sqrt(2)i