What are the solutions to the equation (q)=q^3-30q^2+500q-200 ?

The solutions to the equation (q)=q^3-30q^2+500q-200 are q\approx 0.41080…

Find the zeros of (q)=q^3-30q^2+500q-200

The zeros of (q)=q^3-30q^2+500q-200 are q\approx 0.41080…

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(q) = q^{3} - 30 q^{2} + 500 q - 200

q \approx 0.41080 \dots

Solution steps

(q) = q^{3} - 30 q^{2} + 500 q - 200

Refine

q = q^{3} - 30 q^{2} + 500 q - 200

Switch sides

q^{3} - 30 q^{2} + 500 q - 200 = q

Move

q

to the left side

q^{3} - 30 q^{2} + 499 q - 200 = 0

Find one solution for

q^{3} - 30 q^{2} + 499 q - 200 = 0

using Newton-Raphson:

q \approx 0.41080 \dots

Apply long division:

\frac{q ^{3} - 30 q ^{2} + 499 q - 200}{q - 0.41080 \dots} = q^{2} - 29.58919 \dots q + 486.84450 \dots

q^{2} - 29.58919 \dots q + 486.84450 \dots \approx 0

Find one solution for

q^{2} - 29.58919 \dots q + 486.84450 \dots = 0

using Newton-Raphson:

No Solution for

q \in R

The solution is

q \approx 0.41080 \dots

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

x (x - 2) (x + 3) (x - 12) = 0

(x^{2} + 3 x + 2)^{2} - 8 (x^{2} + 3 x) = 4

x^{6} + 72 x^{3} + 512 = 0

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

What are the solutions to the equation (q)=q^3-30q^2+500q-200 ?
The solutions to the equation (q)=q^3-30q^2+500q-200 are q\approx 0.41080…
Find the zeros of (q)=q^3-30q^2+500q-200
The zeros of (q)=q^3-30q^2+500q-200 are q\approx 0.41080…