What are the solutions to the equation 3x^4-16x^3+24x^2-9=0 ?

The solutions to the equation 3x^4-16x^3+24x^2-9=0 are x\approx 0.84407…,x\approx-0.52104…

Find the zeros of 3x^4-16x^3+24x^2-9=0

The zeros of 3x^4-16x^3+24x^2-9=0 are x\approx 0.84407…,x\approx-0.52104…

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3 x^{4} - 16 x^{3} + 24 x^{2} - 9 = 0

x \approx 0.84407 \dots, x \approx - 0.52104 \dots

Solution steps

3 x^{4} - 16 x^{3} + 24 x^{2} - 9 = 0

Find one solution for

3 x^{4} - 16 x^{3} + 24 x^{2} - 9 = 0

using Newton-Raphson:

x \approx 0.84407 \dots

Apply long division:

\frac{3 x ^{4} - 16 x ^{3} + 24 x ^{2} - 9}{x - 0.84407 \dots} = 3 x^{3} - 13.46776 \dots x^{2} + 12.63215 \dots x + 10.66252 \dots

3 x^{3} - 13.46776 \dots x^{2} + 12.63215 \dots x + 10.66252 \dots \approx 0

Find one solution for

3 x^{3} - 13.46776 \dots x^{2} + 12.63215 \dots x + 10.66252 \dots = 0

using Newton-Raphson:

x \approx - 0.52104 \dots

Apply long division:

\frac{3 x ^{3} - 13.46776 \dots x ^{2} + 12.63215 \dots x + 10.66252 \dots}{x + 0.52104 \dots} = 3 x^{2} - 15.03089 \dots x + 20.46387 \dots

3 x^{2} - 15.03089 \dots x + 20.46387 \dots \approx 0

Find one solution for

3 x^{2} - 15.03089 \dots x + 20.46387 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.84407 \dots, x \approx - 0.52104 \dots

y, x^{3} \cdot y = 9

x^{3} - 2 x^{2} - 6 x - 8

y^{3} - 9 y^{2} + 27 y = 47

9 x^{8} - 9 = 0

x^{3} - x^{2} = 1

What are the solutions to the equation 3x^4-16x^3+24x^2-9=0 ?
The solutions to the equation 3x^4-16x^3+24x^2-9=0 are x\approx 0.84407…,x\approx-0.52104…
Find the zeros of 3x^4-16x^3+24x^2-9=0
The zeros of 3x^4-16x^3+24x^2-9=0 are x\approx 0.84407…,x\approx-0.52104…