Question

3x² + 15x + 11 = 0

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 3\), \(b = 15\), \(c = 11\).

Step2: Use quadratic formula

Quadratic formula: \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)
Calculate discriminant \(\Delta=b^2 - 4ac=(15)^2-4\times3\times11 = 225 - 132 = 93\)
Then \(x=\frac{-15\pm\sqrt{93}}{2\times3}=\frac{-15\pm\sqrt{93}}{6}\)

Answer:

\(x=\frac{-15 + \sqrt{93}}{6}\) or \(x=\frac{-15 - \sqrt{93}}{6}\)