\( \begin{array}{lll}\text { a. }-1,-8 & \text { b. } 7,8 & \text { c. }-7,8 \\ \text { Find the value of the roots for the quadratic equation } x^{2}+11 x+24 \\ \begin{array}{lll}\text { a. } 8,-3 & \text { b. }-8,3 & \text { c. } 8,3\end{array}\end{array} \)

To find the roots of the quadratic equation \( x^2 + 11x + 24 = 0 \), we can use the factoring method or the quadratic formula. First, let's try factoring: We need to find two numbers that multiply to \( 24 \) (the constant term) and add up to \( 11 \) (the coefficient of \( x \)). The pairs of factors of \( 24 \) are: - \( 1 \) and \( 24 \) (sum = 25) - \( 2 \) and \( 12 \) (sum = 14) - \( 3 \) and \( 8 \) (sum = 11) - \( 4 \) and \( 6 \) (sum = 10) The pair \( 3 \) and \( 8 \) works because \( 3 + 8 = 11 \). Thus, we can factor the quadratic as: \[ (x + 3)(x + 8) = 0 \] Setting each factor to zero gives us the roots: \[ x + 3 = 0 \quad \Rightarrow \quad x = -3 \] \[ x + 8 = 0 \quad \Rightarrow \quad x = -8 \] So the roots of the equation \( x^2 + 11x + 24 = 0 \) are \( -3 \) and \( -8 \). Now, looking at the options provided: - a. \( -1, -8 \) - b. \( 7, 8 \) - c. \( -7, 8 \) None of these options match the roots we found. However, if we look at the second part of your question regarding the roots of the quadratic equation \( x^2 + 11x + 24 \), the correct roots are \( -3 \) and \( -8 \), which are not listed in the options provided. If you meant to ask for the roots of a different equation or if there was a mistake in the options, please clarify!