What are the solutions to the equation s^4-6s-15s=3 ?

The solutions to the equation s^4-6s-15s=3 are s\approx-0.14283…,s\approx 2.80498…

Find the zeros of s^4-6s-15s=3

The zeros of s^4-6s-15s=3 are s\approx-0.14283…,s\approx 2.80498…

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s^{4} - 6 s - 15 s = 3

s \approx - 0.14283 \dots, s \approx 2.80498 \dots

Solution steps

s^{4} - 6 s - 15 s = 3

Refine

s^{4} - 21 s = 3

Move

3

to the left side

s^{4} - 21 s - 3 = 0

Find one solution for

s^{4} - 21 s - 3 = 0

using Newton-Raphson:

s \approx - 0.14283 \dots

Apply long division:

\frac{s ^{4} - 21 s - 3}{s + 0.14283 \dots} = s^{3} - 0.14283 \dots s^{2} + 0.02040 \dots s - 21.00291 \dots

s^{3} - 0.14283 \dots s^{2} + 0.02040 \dots s - 21.00291 \dots \approx 0

Find one solution for

s^{3} - 0.14283 \dots s^{2} + 0.02040 \dots s - 21.00291 \dots = 0

using Newton-Raphson:

s \approx 2.80498 \dots

Apply long division:

\frac{s ^{3} - 0.14283 \dots s ^{2} + 0.02040 \dots s - 21.00291 \dots}{s - 2.80498 \dots} = s^{2} + 2.66215 \dots s + 7.48770 \dots

s^{2} + 2.66215 \dots s + 7.48770 \dots \approx 0

Find one solution for

s^{2} + 2.66215 \dots s + 7.48770 \dots = 0

using Newton-Raphson:

No Solution for

s \in R

The solutions are

s \approx - 0.14283 \dots, s \approx 2.80498 \dots

4 x^{3} - 9 x + 2 = 0

4 x^{3} + 4 x^{2} - 9 x - 9 = 0

x^{3} - 2 x^{2} + x - 1 = 0

x^{4} - 6 x^{2} + 4 = 0

(x^{4} - 4) = 0

What are the solutions to the equation s^4-6s-15s=3 ?
The solutions to the equation s^4-6s-15s=3 are s\approx-0.14283…,s\approx 2.80498…
Find the zeros of s^4-6s-15s=3
The zeros of s^4-6s-15s=3 are s\approx-0.14283…,s\approx 2.80498…