What are the solutions to the equation (x-2)(x-5i)(x+5i)=52 ?

The solutions to the equation (x-2)(x-5i)(x+5i)=52 are x\approx 3.41765…

Find the zeros of (x-2)(x-5i)(x+5i)=52

The zeros of (x-2)(x-5i)(x+5i)=52 are x\approx 3.41765…

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(x - 2) (x - 5 i) (x + 5 i) = 52

x \approx 3.41765 \dots

Solution steps

(x - 2) (x - 5 i) (x + 5 i) = 52

Expand

(x - 2) (x - 5 i) (x + 5 i) : x^{3} + 25 x - 2 x^{2} - 50

x^{3} + 25 x - 2 x^{2} - 50 = 52

Move

52

to the left side

x^{3} - 2 x^{2} + 25 x - 102 = 0

Find one solution for

x^{3} - 2 x^{2} + 25 x - 102 = 0

using Newton-Raphson:

x \approx 3.41765 \dots

Apply long division:

\frac{x ^{3} - 2 x ^{2} + 25 x - 102}{x - 3.41765 \dots} = x^{2} + 1.41765 \dots x + 29.84504 \dots

x^{2} + 1.41765 \dots x + 29.84504 \dots \approx 0

Find one solution for

x^{2} + 1.41765 \dots x + 29.84504 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 3.41765 \dots

x^{4} - 48 x^{2} - 49 = 0

s^{4} + 7 s^{3} + 10 s^{2} = 0

x^{3} - 4 x^{2} - 13 x + 52 = 0

- x (x - 9) (4 x + 9) = 0

a^{4} - 2 a^{2} + 1 = 0

What are the solutions to the equation (x-2)(x-5i)(x+5i)=52 ?
The solutions to the equation (x-2)(x-5i)(x+5i)=52 are x\approx 3.41765…
Find the zeros of (x-2)(x-5i)(x+5i)=52
The zeros of (x-2)(x-5i)(x+5i)=52 are x\approx 3.41765…