What are the solutions to the equation 4z(z^2-5)=4z^2-27 ?

The solutions to the equation 4z(z^2-5)=4z^2-27 are z\approx-2.34997…

Find the zeros of 4z(z^2-5)=4z^2-27

The zeros of 4z(z^2-5)=4z^2-27 are z\approx-2.34997…

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4 z (z^{2} - 5) = 4 z^{2} - 27

z \approx - 2.34997 \dots

Solution steps

4 z (z^{2} - 5) = 4 z^{2} - 27

Expand

4 z (z^{2} - 5) : 4 z^{3} - 20 z

4 z^{3} - 20 z = 4 z^{2} - 27

Move

27

to the left side

4 z^{3} - 20 z + 27 = 4 z^{2}

Move

4 z^{2}

to the left side

4 z^{3} - 20 z + 27 - 4 z^{2} = 0

Write in the standard form

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

4 z^{3} - 4 z^{2} - 20 z + 27 = 0

Find one solution for

4 z^{3} - 4 z^{2} - 20 z + 27 = 0

using Newton-Raphson:

z \approx - 2.34997 \dots

Apply long division:

\frac{4 z ^{3} - 4 z ^{2} - 20 z + 27}{z + 2.34997 \dots} = 4 z^{2} - 13.39990 \dots z + 11.48947 \dots

4 z^{2} - 13.39990 \dots z + 11.48947 \dots \approx 0

Find one solution for

4 z^{2} - 13.39990 \dots z + 11.48947 \dots = 0

using Newton-Raphson:

No Solution for

z \in R

The solution is

z \approx - 2.34997 \dots

x^{6} + 4 x^{5} - 5 x^{4} = 0

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

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

x^{3} - 4 x^{2} - 17 x + 60 = 0

(x^{2} + 1) (x^{2} + 4) = 0

What are the solutions to the equation 4z(z^2-5)=4z^2-27 ?
The solutions to the equation 4z(z^2-5)=4z^2-27 are z\approx-2.34997…
Find the zeros of 4z(z^2-5)=4z^2-27
The zeros of 4z(z^2-5)=4z^2-27 are z\approx-2.34997…