What are the solutions to the equation x(x-3)(x-4)-4=0 ?

The solutions to the equation x(x-3)(x-4)-4=0 are x=2,x=(5+sqrt(17))/2 ,x=(5-sqrt(17))/2

Find the zeros of x(x-3)(x-4)-4=0

The zeros of x(x-3)(x-4)-4=0 are x=2,x=(5+sqrt(17))/2 ,x=(5-sqrt(17))/2

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x (x - 3) (x - 4) - 4 = 0

x = 2, x = \frac{5 + 17}{2}, x = \frac{5 - 17}{2}

Decimal Notation

x = 2, x = 4.56155 \dots, x = 0.43844 \dots

Solution steps

x (x - 3) (x - 4) - 4 = 0

Expand

x (x - 3) (x - 4) - 4 : x^{3} - 7 x^{2} + 12 x - 4

x^{3} - 7 x^{2} + 12 x - 4 = 0

Factor

x^{3} - 7 x^{2} + 12 x - 4 : (x - 2) (x^{2} - 5 x + 2)

(x - 2) (x^{2} - 5 x + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 2 = 0 or x^{2} - 5 x + 2 = 0

Solve

x - 2 = 0 : x = 2

Solve

x^{2} - 5 x + 2 = 0 : x = \frac{5 + 17}{2}, x = \frac{5 - 17}{2}

The solutions are

x = 2, x = \frac{5 + 17}{2}, x = \frac{5 - 17}{2}

x^{3} x^{2} = 4 x + 15

2 k^{4} - 3 k^{2} + 5 = 25

x^{4} + 3 x^{2} - 18 = 0

x (2 x^{2} + x - 3) = 10

5 x^{3} + 20 x^{2} + 20 x = 0

What are the solutions to the equation x(x-3)(x-4)-4=0 ?
The solutions to the equation x(x-3)(x-4)-4=0 are x=2,x=(5+sqrt(17))/2 ,x=(5-sqrt(17))/2
Find the zeros of x(x-3)(x-4)-4=0
The zeros of x(x-3)(x-4)-4=0 are x=2,x=(5+sqrt(17))/2 ,x=(5-sqrt(17))/2