Question

1. solve $5x^2 + 3x - 1 = 0$.

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 5\), \(b = 3\), \(c = -1\).

Step2: Use quadratic formula

Quadratic formula: \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)
Substitute values: \(x=\frac{-3\pm\sqrt{3^2 - 4\times5\times(-1)}}{2\times5}\)

Step3: Calculate discriminant

\(b^2 - 4ac = 9 + 20 = 29\)

Step4: Solve for x

\(x=\frac{-3\pm\sqrt{29}}{10}\)

Answer:

\(x = \frac{-3 + \sqrt{29}}{10}\) or \(x = \frac{-3 - \sqrt{29}}{10}\)