Q23 Prep 3 Algebra Question Bank

a) Given the function \( f : f(X) = X^3 - 2X^2 - 75 \)

Prove that: The number 5 is one of the zeroes of the function \( f \)

MR/Nasef.N

Proof:

Substitute \( X = 5 \) into the function:

\[ \begin{align*} f(5) &= 5^3 - 2(5)^2 - 75 \\ &= 125 - 2(25) - 75 \\ &= 125 - 50 - 75 \\ &= 0 \end{align*} \]

Since \( f(5) = 0 \), we conclude that 5 is indeed a zero of the function \( f \).