What are the solutions to the equation x(x-5)^3-14(x-5)^2=0 ?

The solutions to the equation x(x-5)^3-14(x-5)^2=0 are x=5,x=-2,x=7

Find the zeros of x(x-5)^3-14(x-5)^2=0

The zeros of x(x-5)^3-14(x-5)^2=0 are x=5,x=-2,x=7

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x (x - 5)^{3} - 14 (x - 5)^{2} = 0

x = 5, x = - 2, x = 7

Solution steps

x (x - 5)^{3} - 14 (x - 5)^{2} = 0

Factor

x (x - 5)^{3} - 14 (x - 5)^{2} : (x - 5)^{2} (x + 2) (x - 7)

(x - 5)^{2} (x + 2) (x - 7) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 5 = 0 or x + 2 = 0 or x - 7 = 0

Solve

x - 5 = 0 : x = 5

Solve

x + 2 = 0 : x = - 2

Solve

x - 7 = 0 : x = 7

The solutions are

x = 5, x = - 2, x = 7

4 x (x - 3)^{2} (2 x - 5) = 0

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

x^{3} + x^{2} - 7 x + 15 = 0

a x^{3} - 2 x^{2} - 3 x = 0

x^{2} (x - 1) (x + 2) = 0

What are the solutions to the equation x(x-5)^3-14(x-5)^2=0 ?
The solutions to the equation x(x-5)^3-14(x-5)^2=0 are x=5,x=-2,x=7
Find the zeros of x(x-5)^3-14(x-5)^2=0
The zeros of x(x-5)^3-14(x-5)^2=0 are x=5,x=-2,x=7