What are the solutions to the equation 125t^4-180t^3-270t^2+250=0 ?

The solutions to the equation 125t^4-180t^3-270t^2+250=0 are t\approx 2.22854…,t\approx 0.86766…

Find the zeros of 125t^4-180t^3-270t^2+250=0

The zeros of 125t^4-180t^3-270t^2+250=0 are t\approx 2.22854…,t\approx 0.86766…

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125 t^{4} - 180 t^{3} - 270 t^{2} + 250 = 0

t \approx 2.22854 \dots, t \approx 0.86766 \dots

Solution steps

125 t^{4} - 180 t^{3} - 270 t^{2} + 250 = 0

Find one solution for

125 t^{4} - 180 t^{3} - 270 t^{2} + 250 = 0

using Newton-Raphson:

t \approx 2.22854 \dots

Apply long division:

\frac{125 t ^{4} - 180 t ^{3} - 270 t ^{2} + 250}{t - 2.22854 \dots} = 125 t^{3} + 98.56750 \dots t^{2} - 50.33836 \dots t - 112.18106 \dots

125 t^{3} + 98.56750 \dots t^{2} - 50.33836 \dots t - 112.18106 \dots \approx 0

Find one solution for

125 t^{3} + 98.56750 \dots t^{2} - 50.33836 \dots t - 112.18106 \dots = 0

using Newton-Raphson:

t \approx 0.86766 \dots

Apply long division:

\frac{125 t ^{3} + 98.56750 \dots t ^{2} - 50.33836 \dots t - 112.18106 \dots}{t - 0.86766 \dots} = 125 t^{2} + 207.02569 \dots t + 129.29068 \dots

125 t^{2} + 207.02569 \dots t + 129.29068 \dots \approx 0

Find one solution for

125 t^{2} + 207.02569 \dots t + 129.29068 \dots = 0

using Newton-Raphson:

No Solution for

t \in R

The solutions are

t \approx 2.22854 \dots, t \approx 0.86766 \dots

24 x^{3} + 6 x^{2} = 0

y, y - x^{3} = 0

3 x^{4} + 2 x^{2} - 8 = 0

x, x^{3} + y^{3} = a^{3}

x^{4} + x^{3} + x^{2} + x = - 1

What are the solutions to the equation 125t^4-180t^3-270t^2+250=0 ?
The solutions to the equation 125t^4-180t^3-270t^2+250=0 are t\approx 2.22854…,t\approx 0.86766…
Find the zeros of 125t^4-180t^3-270t^2+250=0
The zeros of 125t^4-180t^3-270t^2+250=0 are t\approx 2.22854…,t\approx 0.86766…