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

The solutions to the equation x^4-3x^3+7x-2=0 are x\approx 0.29570…,x\approx-1.38715…

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

The zeros of x^4-3x^3+7x-2=0 are x\approx 0.29570…,x\approx-1.38715…

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

x \approx 0.29570 \dots, x \approx - 1.38715 \dots

Solution steps

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

Find one solution for

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

using Newton-Raphson:

x \approx 0.29570 \dots

Apply long division:

\frac{x ^{4} - 3 x ^{3} + 7 x - 2}{x - 0.29570 \dots} = x^{3} - 2.70429 \dots x^{2} - 0.79966 \dots x + 6.76353 \dots

x^{3} - 2.70429 \dots x^{2} - 0.79966 \dots x + 6.76353 \dots \approx 0

Find one solution for

x^{3} - 2.70429 \dots x^{2} - 0.79966 \dots x + 6.76353 \dots = 0

using Newton-Raphson:

x \approx - 1.38715 \dots

Apply long division:

\frac{x ^{3} - 2.70429 \dots x ^{2} - 0.79966 \dots x + 6.76353 \dots}{x + 1.38715 \dots} = x^{2} - 4.09145 \dots x + 4.87582 \dots

x^{2} - 4.09145 \dots x + 4.87582 \dots \approx 0

Find one solution for

x^{2} - 4.09145 \dots x + 4.87582 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.29570 \dots, x \approx - 1.38715 \dots

x^{4} - 4 x^{3} + 10 = 0

(2 x + 7) (x^{2} - 15) = 0

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

x^{3} + 2 x^{2} - 11 x = 12

(5 x^{2} - 12 x - 9) (4 x + a) = 0

What are the solutions to the equation x^4-3x^3+7x-2=0 ?
The solutions to the equation x^4-3x^3+7x-2=0 are x\approx 0.29570…,x\approx-1.38715…
Find the zeros of x^4-3x^3+7x-2=0
The zeros of x^4-3x^3+7x-2=0 are x\approx 0.29570…,x\approx-1.38715…