Questions: Select the correct answer. What are the solutions of the quadratic equation below? 2 x^2 - 2 x - 9 = 0 A. (-1 ± √19)/2 B. (3 ± √19)/2 C. (1 ± √19)/2 D. (1 ± 3√19)/2

Solution Steps

The quadratic equation is given as: \[ 2x^{2} - 2x - 9 = 0 \] Here, the coefficients are:

• \( a = 2 \)
• \( b = -2 \)
• \( c = -9 \)

The quadratic formula is: \[ x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a} \] Substitute the values of \( a \), \( b \), and \( c \) into the formula: \[ x = \frac{-(-2) \pm \sqrt{(-2)^{2} - 4 \cdot 2 \cdot (-9)}}{2 \cdot 2} \]

Calculate the discriminant and simplify: \[ x = \frac{2 \pm \sqrt{4 + 72}}{4} \] \[ x = \frac{2 \pm \sqrt{76}}{4} \] \[ x = \frac{2 \pm 2\sqrt{19}}{4} \] \[ x = \frac{1 \pm \sqrt{19}}{2} \]

Final Answer