Question

find the solutions of the quadratic equation $5x^2 + 3x + 1 = 0$. choose 1 answer: a $-\frac{3}{10} pm \frac{sqrt{29}}{10}i$ b $-\frac{3}{10} pm \frac{sqrt{29}}{10}$ c $-\frac{3}{10} pm \frac{sqrt{11}}{10}i$ d $\frac{3}{10} pm \frac{sqrt{11}}{10}i$

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, \(a = 5\), \(b = 3\), \(c = 1\).

Step2: Calculate the Discriminant

Discriminant \(D=b^{2}-4ac=(3)^{2}-4\times5\times1 = 9 - 20=- 11\).

Step3: Substitute into Quadratic Formula

Since \(D=-11\), we have \(x=\frac{-3\pm\sqrt{-11}}{2\times5}=\frac{-3\pm i\sqrt{11}}{10}=-\frac{3}{10}\pm\frac{\sqrt{11}}{10}i\).

Answer:

C. \(-\frac{3}{10}\pm\frac{\sqrt{11}}{10}i\)