What are the solutions to the equation g(n)=n^3-5n^2,g(-4n) ?

The solutions to the equation g(n)=n^3-5n^2,g(-4n) are n=0,n=(5+sqrt(25+4g))/2 ,n=(5-sqrt(25+4g))/2

Find the zeros of g(n)=n^3-5n^2,g(-4n)

The zeros of g(n)=n^3-5n^2,g(-4n) are n=0,n=(5+sqrt(25+4g))/2 ,n=(5-sqrt(25+4g))/2

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g (n) = n^{3} - 5 n^{2}, g (- 4 n)

n = 0, n = \frac{5 + 25 + 4 g}{2}, n = \frac{5 - 25 + 4 g}{2}

Solution steps

g (n) = n^{3} - 5 n^{2}, g (- 4 n)

Refine

g n = n^{3} - 5 n^{2}

Switch sides

n^{3} - 5 n^{2} = g n

Move

g n

to the left side

n^{3} - 5 n^{2} - g n = 0

Factor

n^{3} - 5 n^{2} - g n : n (n^{2} - 5 n - g)

n (n^{2} - 5 n - g) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

n = 0 or n^{2} - 5 n - g = 0

Solve

n^{2} - 5 n - g = 0 : n = \frac{5 + 25 + 4 g}{2}, n = \frac{5 - 25 + 4 g}{2}

The solutions are

n = 0, n = \frac{5 + 25 + 4 g}{2}, n = \frac{5 - 25 + 4 g}{2}

(x^{2} + x + 3) (x^{2} - x + 3) = 45

x^{4} + 9 x^{2} = 0

n^{3} + 2 n^{2} - 35 n = 0

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

12 - 2 x = x^{2} - 4 x^{9}

What are the solutions to the equation g(n)=n^3-5n^2,g(-4n) ?
The solutions to the equation g(n)=n^3-5n^2,g(-4n) are n=0,n=(5+sqrt(25+4g))/2 ,n=(5-sqrt(25+4g))/2
Find the zeros of g(n)=n^3-5n^2,g(-4n)
The zeros of g(n)=n^3-5n^2,g(-4n) are n=0,n=(5+sqrt(25+4g))/2 ,n=(5-sqrt(25+4g))/2