What are the solutions to the equation 3x^1-5x^2+4x^3=7 ?

The solutions to the equation 3x^1-5x^2+4x^3=7 are x\approx 1.51643…

Find the zeros of 3x^1-5x^2+4x^3=7

The zeros of 3x^1-5x^2+4x^3=7 are x\approx 1.51643…

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3 x^{1} - 5 x^{2} + 4 x^{3} = 7

x \approx 1.51643 \dots

Solution steps

3 x^{1} - 5 x^{2} + 4 x^{3} = 7

Refine

3 x - 5 x^{2} + 4 x^{3} = 7

Move

7

to the left side

3 x - 5 x^{2} + 4 x^{3} - 7 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

4 x^{3} - 5 x^{2} + 3 x - 7 = 0

Find one solution for

4 x^{3} - 5 x^{2} + 3 x - 7 = 0

using Newton-Raphson:

x \approx 1.51643 \dots

Apply long division:

\frac{4 x ^{3} - 5 x ^{2} + 3 x - 7}{x - 1.51643 \dots} = 4 x^{2} + 1.06572 \dots x + 4.61610 \dots

4 x^{2} + 1.06572 \dots x + 4.61610 \dots \approx 0

Find one solution for

4 x^{2} + 1.06572 \dots x + 4.61610 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 1.51643 \dots

x^{3} - 5 x^{2} = - 6 x

8 x^{3} - 16 x^{2} - 16 x - 2 = 0

x^{5} - 81 x = 0

6 x^{3} - 21 x^{2} - 12 x = 0

p^{3} - 4 p = 0

What are the solutions to the equation 3x^1-5x^2+4x^3=7 ?
The solutions to the equation 3x^1-5x^2+4x^3=7 are x\approx 1.51643…
Find the zeros of 3x^1-5x^2+4x^3=7
The zeros of 3x^1-5x^2+4x^3=7 are x\approx 1.51643…