What are the solutions to the equation 34x^4-7x^2-3x+1=0 ?

The solutions to the equation 34x^4-7x^2-3x+1=0 are x\approx 0.23768…,x\approx 0.51617…

Find the zeros of 34x^4-7x^2-3x+1=0

The zeros of 34x^4-7x^2-3x+1=0 are x\approx 0.23768…,x\approx 0.51617…

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34 x^{4} - 7 x^{2} - 3 x + 1 = 0

x \approx 0.23768 \dots, x \approx 0.51617 \dots

Solution steps

34 x^{4} - 7 x^{2} - 3 x + 1 = 0

Find one solution for

34 x^{4} - 7 x^{2} - 3 x + 1 = 0

using Newton-Raphson:

x \approx 0.23768 \dots

Apply long division:

\frac{34 x ^{4} - 7 x ^{2} - 3 x + 1}{x - 0.23768 \dots} = 34 x^{3} + 8.08128 \dots x^{2} - 5.07919 \dots x - 4.20724 \dots

34 x^{3} + 8.08128 \dots x^{2} - 5.07919 \dots x - 4.20724 \dots \approx 0

Find one solution for

34 x^{3} + 8.08128 \dots x^{2} - 5.07919 \dots x - 4.20724 \dots = 0

using Newton-Raphson:

x \approx 0.51617 \dots

Apply long division:

\frac{34 x ^{3} + 8.08128 \dots x ^{2} - 5.07919 \dots x - 4.20724 \dots}{x - 0.51617 \dots} = 34 x^{2} + 25.63113 \dots x + 8.15086 \dots

34 x^{2} + 25.63113 \dots x + 8.15086 \dots \approx 0

Find one solution for

34 x^{2} + 25.63113 \dots x + 8.15086 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.23768 \dots, x \approx 0.51617 \dots

x^{3} - 4 x^{2} - 3 x + 18 = 0

3 (c^{2})^{2} + 10 c - 6 = 0

x^{3} - 14 x + 8 = 0

y^{4} - 9 = 0

d^{4} + 18 d^{2} + 81 = 0

What are the solutions to the equation 34x^4-7x^2-3x+1=0 ?
The solutions to the equation 34x^4-7x^2-3x+1=0 are x\approx 0.23768…,x\approx 0.51617…
Find the zeros of 34x^4-7x^2-3x+1=0
The zeros of 34x^4-7x^2-3x+1=0 are x\approx 0.23768…,x\approx 0.51617…