What are the solutions to the equation x^3+3x^2-112=0 ?

The solutions to the equation x^3+3x^2-112=0 are x=4,x=-7/2+i(3sqrt(7))/2 ,x=-7/2-i(3sqrt(7))/2

Find the zeros of x^3+3x^2-112=0

The zeros of x^3+3x^2-112=0 are x=4,x=-7/2+i(3sqrt(7))/2 ,x=-7/2-i(3sqrt(7))/2

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x^{3} + 3 x^{2} - 112 = 0

x = 4, x = - \frac{7}{2} + i \frac{3 7}{2}, x = - \frac{7}{2} - i \frac{3 7}{2}

Solution steps

x^{3} + 3 x^{2} - 112 = 0

Factor

x^{3} + 3 x^{2} - 112 : (x - 4) (x^{2} + 7 x + 28)

(x - 4) (x^{2} + 7 x + 28) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 4 = 0 or x^{2} + 7 x + 28 = 0

Solve

x - 4 = 0 : x = 4

Solve

x^{2} + 7 x + 28 = 0 : x = - \frac{7}{2} + i \frac{3 7}{2}, x = - \frac{7}{2} - i \frac{3 7}{2}

The solutions are

x = 4, x = - \frac{7}{2} + i \frac{3 7}{2}, x = - \frac{7}{2} - i \frac{3 7}{2}

x^{4} - \frac{6}{7} x^{2} + \frac{3}{35} = 0

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

5 x^{4} + 7 x^{2} - 12 = 0

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

x^{16} + 5 x^{8} + 4 = 0

What are the solutions to the equation x^3+3x^2-112=0 ?
The solutions to the equation x^3+3x^2-112=0 are x=4,x=-7/2+i(3sqrt(7))/2 ,x=-7/2-i(3sqrt(7))/2
Find the zeros of x^3+3x^2-112=0
The zeros of x^3+3x^2-112=0 are x=4,x=-7/2+i(3sqrt(7))/2 ,x=-7/2-i(3sqrt(7))/2