What are the solutions to the equation (x-3)(x-3)(x-4)(x-5)=105 ?

The solutions to the equation (x-3)(x-3)(x-4)(x-5)=105 are x\approx 0.45023…,x\approx 7.06803…

Find the zeros of (x-3)(x-3)(x-4)(x-5)=105

The zeros of (x-3)(x-3)(x-4)(x-5)=105 are x\approx 0.45023…,x\approx 7.06803…

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(x - 3) (x - 3) (x - 4) (x - 5) = 105

x \approx 0.45023 \dots, x \approx 7.06803 \dots

Solution steps

(x - 3) (x - 3) (x - 4) (x - 5) = 105

Expand

(x - 3) (x - 3) (x - 4) (x - 5) : x^{4} - 15 x^{3} + 83 x^{2} - 201 x + 180

x^{4} - 15 x^{3} + 83 x^{2} - 201 x + 180 = 105

Move

105

to the left side

x^{4} - 15 x^{3} + 83 x^{2} - 201 x + 75 = 0

Find one solution for

x^{4} - 15 x^{3} + 83 x^{2} - 201 x + 75 = 0

using Newton-Raphson:

x \approx 0.45023 \dots

Apply long division:

\frac{x ^{4} - 15 x ^{3} + 83 x ^{2} - 201 x + 75}{x - 0.45023 \dots} = x^{3} - 14.54976 \dots x^{2} + 76.44919 \dots x - 166.57995 \dots

x^{3} - 14.54976 \dots x^{2} + 76.44919 \dots x - 166.57995 \dots \approx 0

Find one solution for

x^{3} - 14.54976 \dots x^{2} + 76.44919 \dots x - 166.57995 \dots = 0

using Newton-Raphson:

x \approx 7.06803 \dots

Apply long division:

\frac{x ^{3} - 14.54976 \dots x ^{2} + 76.44919 \dots x - 166.57995 \dots}{x - 7.06803 \dots} = x^{2} - 7.48172 \dots x + 23.56806 \dots

x^{2} - 7.48172 \dots x + 23.56806 \dots \approx 0

Find one solution for

x^{2} - 7.48172 \dots x + 23.56806 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.45023 \dots, x \approx 7.06803 \dots

2 x^{3} + 3 = 0

x^{4} - 3 x^{3} - 6 x^{2} - 28 x - 24 = 0

(x - 10) (x^{2} + 64) = 0

0 = x^{3} + 3

0 = x^{3} + x

What are the solutions to the equation (x-3)(x-3)(x-4)(x-5)=105 ?
The solutions to the equation (x-3)(x-3)(x-4)(x-5)=105 are x\approx 0.45023…,x\approx 7.06803…
Find the zeros of (x-3)(x-3)(x-4)(x-5)=105
The zeros of (x-3)(x-3)(x-4)(x-5)=105 are x\approx 0.45023…,x\approx 7.06803…