What are the solutions to the equation 5x^4-19x+3=2x-1 ?

The solutions to the equation 5x^4-19x+3=2x-1 are x\approx 0.19079…,x\approx 1.54415…

Find the zeros of 5x^4-19x+3=2x-1

The zeros of 5x^4-19x+3=2x-1 are x\approx 0.19079…,x\approx 1.54415…

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5 x^{4} - 19 x + 3 = 2 x - 1

x \approx 0.19079 \dots, x \approx 1.54415 \dots

Solution steps

5 x^{4} - 19 x + 3 = 2 x - 1

Move

1

to the left side

5 x^{4} - 19 x + 4 = 2 x

Move

2 x

to the left side

5 x^{4} - 21 x + 4 = 0

Find one solution for

5 x^{4} - 21 x + 4 = 0

using Newton-Raphson:

x \approx 0.19079 \dots

Apply long division:

\frac{5 x ^{4} - 21 x + 4}{x - 0.19079 \dots} = 5 x^{3} + 0.95395 \dots x^{2} + 0.18200 \dots x - 20.96527 \dots

5 x^{3} + 0.95395 \dots x^{2} + 0.18200 \dots x - 20.96527 \dots \approx 0

Find one solution for

5 x^{3} + 0.95395 \dots x^{2} + 0.18200 \dots x - 20.96527 \dots = 0

using Newton-Raphson:

x \approx 1.54415 \dots

Apply long division:

\frac{5 x ^{3} + 0.95395 \dots x ^{2} + 0.18200 \dots x - 20.96527 \dots}{x - 1.54415 \dots} = 5 x^{2} + 8.67474 \dots x + 13.57716 \dots

5 x^{2} + 8.67474 \dots x + 13.57716 \dots \approx 0

Find one solution for

5 x^{2} + 8.67474 \dots x + 13.57716 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.19079 \dots, x \approx 1.54415 \dots

x^{3} - 11 x^{2} + 37 x - 42 = 0

- X^{3} + 9 X^{2} - 24 X + 20 = 0

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

(5 x - 2)^{3} - (5 x - 2) = 0

(x + 1)^{3} + x + 1 = 0

What are the solutions to the equation 5x^4-19x+3=2x-1 ?
The solutions to the equation 5x^4-19x+3=2x-1 are x\approx 0.19079…,x\approx 1.54415…
Find the zeros of 5x^4-19x+3=2x-1
The zeros of 5x^4-19x+3=2x-1 are x\approx 0.19079…,x\approx 1.54415…