Question

find the solutions of the quadratic equation $2x^2 + 6x - 2 = 0$. choose 1 answer: a $-\frac{3}{2} pm \frac{sqrt{13}}{2}i$ b $-\frac{3}{2} pm \frac{sqrt{13}}{2}$ c $-\frac{3}{4} pm \frac{sqrt{13}}{4}$ d $\frac{3}{2} pm \frac{sqrt{13}}{2}$

Explanation:

Step1: Recall quadratic formula

For \(ax^2 + bx + c = 0\), solutions are \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\).
Here, \(a = 2\), \(b = 6\), \(c=-2\).

Step2: Calculate discriminant \(D = b^2 - 4ac\)

\(D = 6^2 - 4\times2\times(-2)=36 + 16 = 52\).

Step3: Simplify \(\sqrt{D}\)

\(\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}\).

Step4: Apply quadratic formula

\(x=\frac{-6\pm2\sqrt{13}}{2\times2}=\frac{-6\pm2\sqrt{13}}{4}\).
Simplify: \(x=\frac{-3\pm\sqrt{13}}{2}=-\frac{3}{2}\pm\frac{\sqrt{13}}{2}\).

Answer:

B. \(-\frac{3}{2}\pm\frac{\sqrt{13}}{2}\)