What are the solutions to the equation (x^2-3x+2)(x^2-9x+20)(x^2-9x+18)=720 ?

The solutions to the equation (x^2-3x+2)(x^2-9x+20)(x^2-9x+18)=720 are x=0,x=7

Find the zeros of (x^2-3x+2)(x^2-9x+20)(x^2-9x+18)=720

The zeros of (x^2-3x+2)(x^2-9x+20)(x^2-9x+18)=720 are x=0,x=7

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(x^{2} - 3 x + 2) (x^{2} - 9 x + 20) (x^{2} - 9 x + 18) = 720

x = 0, x = 7

Solution steps

(x^{2} - 3 x + 2) (x^{2} - 9 x + 20) (x^{2} - 9 x + 18) = 720

Expand

(x^{2} - 3 x + 2) (x^{2} - 9 x + 20) (x^{2} - 9 x + 18) : x^{6} - 21 x^{5} + 175 x^{4} - 735 x^{3} + 1624 x^{2} - 1764 x + 720

x^{6} - 21 x^{5} + 175 x^{4} - 735 x^{3} + 1624 x^{2} - 1764 x + 720 = 720

Move

720

to the left side

x^{6} - 21 x^{5} + 175 x^{4} - 735 x^{3} + 1624 x^{2} - 1764 x = 0

Factor

x^{6} - 21 x^{5} + 175 x^{4} - 735 x^{3} + 1624 x^{2} - 1764 x : x (x - 7) (x^{4} - 14 x^{3} + 77 x^{2} - 196 x + 252)

x (x - 7) (x^{4} - 14 x^{3} + 77 x^{2} - 196 x + 252) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 7 = 0 or x^{4} - 14 x^{3} + 77 x^{2} - 196 x + 252 = 0

Solve

x - 7 = 0 : x = 7

Solve

x^{4} - 14 x^{3} + 77 x^{2} - 196 x + 252 = 0 :

No Solution for

x \in R

The solutions are

x = 0, x = 7

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

(x - 2)^{4} = 0

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

x^{4} - 8 x^{2} + 2 = 0

2 x^{4} + 6 = 0

What are the solutions to the equation (x^2-3x+2)(x^2-9x+20)(x^2-9x+18)=720 ?
The solutions to the equation (x^2-3x+2)(x^2-9x+20)(x^2-9x+18)=720 are x=0,x=7
Find the zeros of (x^2-3x+2)(x^2-9x+20)(x^2-9x+18)=720
The zeros of (x^2-3x+2)(x^2-9x+20)(x^2-9x+18)=720 are x=0,x=7