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If the three real zeros of a function f(x) are located at x = r, x = q, and x = p, determine (if possible) the zeros of the function f(x -5).

User Jmag
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1 Answer

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From the question;

we are give the three zeros of the function f(x) to be located as


x\text{ = r, x = q and x = p}

since r, q and p are zeros of the function f(x) then


(x\text{ - r), ( x - q) and ( x - p)}

are factors of the function f(x)

Therefore

f(x) will be the product of the three factors


F(x)\text{ =(x - r)(x - q)(x - p)}

Given f(x) we can get f(x - 5) as


\begin{gathered} f(x\text{ - 5) = (x - 5 - r)(x - 5 - q)(x - 5 - p)} \\ f(x\text{ - 5) =}(x\text{ - (5 + r))(x - (5 + q))(x - (5 + p))} \end{gathered}

To get the zeros of the function f(x - 5) we equate it to zero

Therefore


(x\text{ - (5 + r))(x - (5 + q))(x - (5 + p)) = 0}

hence


\begin{gathered} (x\text{ - (5 + r)) = 0 implies x = 5 + r} \\ (x\text{ - (5 + q)) = 0 implies x = 5 + q} \\ (x\text{ -(5 + p)) = 0 implies x = 5 + p} \end{gathered}

Therefore, the zeros of the function f(x - 5) are

5 + r, 5 + q and 5 + p

User Aravinthan K
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