If the three solutions of the equation f(x) = 0 are -2, 0, and 3, what are the three solutions of the equation f(x - 2) = 0?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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The solutions of f(x) = 0 are -2, 0 and 3.

So we can write f(x) = (x + 2)( x - 0)(x - 3)

We need the solutions of f(x - 2)

f(x - 2) = (x - 2 + 2)(x - 2 - 0)(x - 2 - 3)

=> f(x - 2) = x(x - 2)(x - 5)

equating each of the factors to 0 we get

x = 0

x - 2 = 0 => x = 2

x - 5 = 0 => x = 5

The required solutions of f(x - 2) are x = 0 , x = 2 and x = 5

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

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Given that 0, -2, and 3 are the zeros of the function f(x).

Then x, (x+2), and (x-3) are the factors of f(x).

Then f(x) = x(x-3)(x+2).

Now we need to find the solutions for f(x-2)

Then, we will substitute with (x-2) in place of x into the equation.

==> f(x-2) = (x-2) ( x-2 -3) (x-2+2)

==> f(x-2) = (x-2)(x-5)(x)

Then the zeros of f(x-2) are 2, 5, and 0

Then the solution for f(x-2) are 0, 2, and 5.

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