What are the solutions to the equation 4pir^4+pir^3-2000r+1000=0 ?

The solutions to the equation 4pir^4+pir^3-2000r+1000=0 are r\approx 0.50059…,r\approx 5.15607…

Find the zeros of 4pir^4+pir^3-2000r+1000=0

The zeros of 4pir^4+pir^3-2000r+1000=0 are r\approx 0.50059…,r\approx 5.15607…

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4 π r^{4} + π r^{3} - 2000 r + 1000 = 0

r \approx 0.50059 \dots, r \approx 5.15607 \dots

Solution steps

4 π r^{4} + π r^{3} - 2000 r + 1000 = 0

Find one solution for

12.56637 \dots r^{4} + 3.14159 \dots r^{3} - 2000 r + 1000 = 0

using Newton-Raphson:

r \approx 0.50059 \dots

Apply long division:

\frac{4 π r ^{4} + π r ^{3} - 2000 r + 1000}{r - 0.50059 \dots} = 12.56637 \dots r^{3} + 9.43221 \dots r^{2} + 4.72168 \dots r - 1997.63636 \dots

12.56637 \dots r^{3} + 9.43221 \dots r^{2} + 4.72168 \dots r - 1997.63636 \dots \approx 0

Find one solution for

12.56637 \dots r^{3} + 9.43221 \dots r^{2} + 4.72168 \dots r - 1997.63636 \dots = 0

using Newton-Raphson:

r \approx 5.15607 \dots

Apply long division:

\frac{12.56637 \dots r ^{3} + 9.43221 \dots r ^{2} + 4.72168 \dots r - 1997.63636 \dots}{r - 5.15607 \dots} = 12.56637 \dots r^{2} + 74.22538 \dots r + 387.43342 \dots

12.56637 \dots r^{2} + 74.22538 \dots r + 387.43342 \dots \approx 0

Find one solution for

12.56637 \dots r^{2} + 74.22538 \dots r + 387.43342 \dots = 0

using Newton-Raphson:

No Solution for

r \in R

The solutions are

r \approx 0.50059 \dots, r \approx 5.15607 \dots

s^{4} + 29 s^{2} + 60 s + 10 = 0

(2 x - 1)^{3} + 12 (x - 1) (x + 1) = 14 x - 13

x^{3} + 6 = - 12

4 x^{3} = 12

x^{4} = 50625

What are the solutions to the equation 4pir^4+pir^3-2000r+1000=0 ?
The solutions to the equation 4pir^4+pir^3-2000r+1000=0 are r\approx 0.50059…,r\approx 5.15607…
Find the zeros of 4pir^4+pir^3-2000r+1000=0
The zeros of 4pir^4+pir^3-2000r+1000=0 are r\approx 0.50059…,r\approx 5.15607…