Question

question 10 of 10
what are the solutions of $2x^2 - 6x + 5 = 0$?

a. $x = \frac{3 + i}{2}$ or $x = \frac{3 - i}{2}$

b. $x = \frac{2 + i}{3}$ or $x = \frac{2 - i}{3}$

c. $x = 3 + i$ or $x = 3 - i$

d. $x = 2 + i$ or $x = 2 - i$

Explanation:

Step1: Recall Quadratic Formula

For a quadratic equation \(ax^2 + bx + c = 0\), the solutions are given by \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). Here, \(a = 2\), \(b=-6\), \(c = 5\).

Step2: Calculate Discriminant (\(D\))

Discriminant \(D=b^2 - 4ac\). Substitute values: \(D=(-6)^2-4\times2\times5=36 - 40=-4\).

Step3: Substitute into Quadratic Formula

\(x=\frac{-(-6)\pm\sqrt{-4}}{2\times2}=\frac{6\pm2i}{4}\) (since \(\sqrt{-4}=2i\)).

Step4: Simplify the Expression

Simplify \(\frac{6\pm2i}{4}=\frac{3\pm i}{2}\), so \(x=\frac{3 + i}{2}\) or \(x=\frac{3 - i}{2}\).

Answer:

A. \(x=\frac{3 + i}{2}\) or \(x=\frac{3 - i}{2}\)