**#9.) which expression correctly shows the solutions of y = x² + 11x + 24?\na.) x = 12, 2\nb.) x = 8…

**#9.) which expression correctly shows the solutions of y = x² + 11x + 24?\na.) x = 12, 2\nb.) x = 8, 3\nc.) x = -2, -12\nd.) x = -3, -8

**#9.) which expression correctly shows the solutions of y = x² + 11x + 24?\na.) x = 12, 2\nb.) x = 8, 3\nc.) x = -2, -12\nd.) x = -3, -8

Answer

Explanation:

Step1: Recall quadratic - formula

For a quadratic equation $y = ax^{2}+bx + c$, the solutions for $x$ are given by $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. In the equation $y=x^{2}+11x + 24$, we have $a = 1$, $b=11$, and $c = 24$.

Step2: Calculate the discriminant

The discriminant $\Delta=b^{2}-4ac=(11)^{2}-4\times1\times24=121 - 96=25$.

Step3: Find the solutions

$x=\frac{-b\pm\sqrt{\Delta}}{2a}=\frac{-11\pm\sqrt{25}}{2\times1}=\frac{-11\pm5}{2}$. When we take the plus - sign: $x=\frac{-11 + 5}{2}=\frac{-6}{2}=-3$. When we take the minus - sign: $x=\frac{-11-5}{2}=\frac{-16}{2}=-8$.

Answer:

d. $x=-3,-8$