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To find the zeros of the quadratic function \( f(x) = x^2 - 10x + 21 \), we need to solve the equation \( x^2 - 10x + 21 = 0 \).

We can attempt to factorize the quadratic expression. We look for two numbers that multiply to 21 and add to -10. These numbers are -3 and -7. Therefore, we can write the factorization as:
\[
x^2 - 10x + 21 = (x - 3)(x - 7)
\]
Setting each factor to zero gives:
\[
x - 3 = 0 \quad \text{or} \quad x - 7 = 0
\]
Thus, \( x = 3 \) and \( x = 7 \).

**Answer:** The zeros of the function are \( x = 3 \) and \( x = 7 \), so the correct selections would be the checkboxes for 3 and 7.

Would you like any further details on this solution, or do you have any other questions about the function?

Here are some follow-up questions:
1. Would you like to learn how to complete the square for this quadratic function?
2. Are you interested in checking whether there are any points of intersection with the x-axis for values other than the zeros found?
3. Would you like to explore how the graph of this quadratic function looks like?
4. Do you need help with any other quadratic functions?
5. Would you like to see the vertex form of this quadratic equation?

**Tip:** When factoring quadratic expressions, always check if the constant term (in this case, 21) can be factorized into two integers whose sum equals the coefficient of the linear term (in this case, -10). This often simplifies finding the roots of the equation.

What are the zeros of the function f(x) = x^2 - 10x + 21?

Learn how to solve the quadratic equation f(x) = x^2 - 10x + 21 by factoring. This example demonstrates key algebraic techniques for factoring and solving quadratic equations. Suitable for Grades 8-10 students.

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