What are the solutions to the equation 3t^4-4t^3-12t^2+6=0 ?

The solutions to the equation 3t^4-4t^3-12t^2+6=0 are t\approx 0.67082…,t\approx 2.70920…

Find the zeros of 3t^4-4t^3-12t^2+6=0

The zeros of 3t^4-4t^3-12t^2+6=0 are t\approx 0.67082…,t\approx 2.70920…

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3 t^{4} - 4 t^{3} - 12 t^{2} + 6 = 0

t \approx 0.67082 \dots, t \approx 2.70920 \dots

Solution steps

3 t^{4} - 4 t^{3} - 12 t^{2} + 6 = 0

Find one solution for

3 t^{4} - 4 t^{3} - 12 t^{2} + 6 = 0

using Newton-Raphson:

t \approx 0.67082 \dots

Apply long division:

\frac{3 t ^{4} - 4 t ^{3} - 12 t ^{2} + 6}{t - 0.67082 \dots} = 3 t^{3} - 1.98753 \dots t^{2} - 13.33328 \dots t - 8.94425 \dots

3 t^{3} - 1.98753 \dots t^{2} - 13.33328 \dots t - 8.94425 \dots \approx 0

Find one solution for

3 t^{3} - 1.98753 \dots t^{2} - 13.33328 \dots t - 8.94425 \dots = 0

using Newton-Raphson:

t \approx 2.70920 \dots

Apply long division:

\frac{3 t ^{3} - 1.98753 \dots t ^{2} - 13.33328 \dots t - 8.94425 \dots}{t - 2.70920 \dots} = 3 t^{2} + 6.14007 \dots t + 3.30143 \dots

3 t^{2} + 6.14007 \dots t + 3.30143 \dots \approx 0

Find one solution for

3 t^{2} + 6.14007 \dots t + 3.30143 \dots = 0

using Newton-Raphson:

No Solution for

t \in R

The solutions are

t \approx 0.67082 \dots, t \approx 2.70920 \dots

x^{3} - 5 x + 1 = - 1.2

- x^{3} + x^{2} + 6 x + 4 = 0

2 x^{3} - 5 x^{2} + 50 x - 125 = 0

- 14 x^{3} + 21 x^{2} - 3 = 0

x^{5} = 5 x - 4 x^{3}

What are the solutions to the equation 3t^4-4t^3-12t^2+6=0 ?
The solutions to the equation 3t^4-4t^3-12t^2+6=0 are t\approx 0.67082…,t\approx 2.70920…
Find the zeros of 3t^4-4t^3-12t^2+6=0
The zeros of 3t^4-4t^3-12t^2+6=0 are t\approx 0.67082…,t\approx 2.70920…