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To find the zeros of the function \(f(x) = x^2 + 2x - 24\), we need to set the function equal to zero and solve for \(x\). The zeros of a function are the values of \(x\) that make the function equal to zero.
So, we have:
\(x^2 + 2x - 24 = 0\)
To factor this quadratic equation, we look for two numbers that multiply to -24 and add up to 2. The numbers that fit these criteria are 6 and -4. Therefore, we can rewrite the equation as:
\(x^2 + 6x - 4x - 24 = 0\)
Now, we factor by grouping:
\(x(x + 6) - 4(x + 6) = 0\)
Factor out the common factor:
\((x - 4)(x + 6) = 0\)
Set each factor to zero to find the zeros:
\(x - 4 = 0\) or \(x + 6 = 0\)
Solving for \(x\), we get:
\(x = 4\) or \(x = -6\)
Therefore, the zeros of the function \(f(x) = x^2 + 2x - 24\) are \(x = 4\) and \(x = -6\).
So, the correct answer is:
B. -6 and 4
I hope this helps you understand how to find the zeros of a quadratic function! If you have any more questions or need further clarification, feel free to ask.
