Question

multiple answer 20 points solve using the quadratic formula: (there are two solutions) 2x² - 2x - 24 = 0 x = -4 x = -2 x = 4 x = 5 x = 3 x = -3

Explanation:

Step1: Identify coefficients

For the quadratic equation $2x^{2}-2x - 24=0$, we have $a = 2$, $b=-2$, $c=-24$.

Step2: Calculate the discriminant

The discriminant $\Delta=b^{2}-4ac=(-2)^{2}-4\times2\times(-24)=4 + 192 = 196$.

Step3: Apply the quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{\Delta}}{2a}$. Substitute the values: $x=\frac{-(-2)\pm\sqrt{196}}{2\times2}=\frac{2\pm14}{4}$.

Step4: Find the two solutions

For the plus - case: $x=\frac{2 + 14}{4}=\frac{16}{4}=4$.
For the minus - case: $x=\frac{2-14}{4}=\frac{-12}{4}=-3$.

Answer:

C. $x = 4$, F. $x=-3$