Questions: FIND THE ERROR Hakeem and Nandi were asked to find the location of the root of the quadratic function represented by the table. Is either of them correct? x -4 -2 0 2 4 6 8 10 f(x) 52 26 8 -2 -4 2 16 38

FIND THE ERROR Hakeem and Nandi were asked to find the location of the root of the quadratic function represented by the table. Is either of them correct? x -4 -2 0 2 4 6 8 10 f(x) 52 26 8 -2 -4 2 16 38
Transcript text: FIND THE ERROR Hakeem and Nandi were asked to find the location of the roo the quadratic function represented by the table. Is either of them correct? \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline$x$ & -4 & -2 & 0 & 2 & 4 & 6 & 8 & 10 \\ \hline$f(x)$ & 52 & 26 & 8 & -2 & -4 & 2 & 16 & 38 \\ \hline \end{tabular}
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Solution

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Solution Steps

Solution Approach

To find the roots of the quadratic function represented by the table, we need to identify the x-values where the function f(x) equals zero. We will iterate through the given x-values and check the corresponding f(x) values to see if any of them are zero. If none of the f(x) values are zero, it indicates that the roots are not explicitly listed in the table.

Step 1: Identify the Roots

To find the roots of the quadratic function represented by the table, we need to determine the values of \( x \) for which \( f(x) = 0 \). The given \( x \) values are \( -4, -2, 0, 2, 4, 6, 8, 10 \) and their corresponding \( f(x) \) values are \( 52, 26, 8, -2, -4, 2, 16, 38 \).

Step 2: Analyze the Function Values

We check each \( f(x) \) value:

  • \( f(-4) = 52 \)
  • \( f(-2) = 26 \)
  • \( f(0) = 8 \)
  • \( f(2) = -2 \)
  • \( f(4) = -4 \)
  • \( f(6) = 2 \)
  • \( f(8) = 16 \)
  • \( f(10) = 38 \)

None of these values equal zero, indicating that there are no roots among the provided \( x \) values.

Step 3: Conclusion

Since there are no \( x \) values for which \( f(x) = 0 \), we conclude that the roots of the quadratic function are not present in the given table.

Final Answer

\(\boxed{\text{No roots found in the table}}\)

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