Question

homework 9: section 2.5
score: 160/280 answered: 16/28
question 19
solve the equation: $5r^2 + r + 5 = 0$. fully simplify all answers, including non - real solutions.
r =

Explanation:

Step1: Identify coefficients

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

Step2: Use quadratic formula

Quadratic formula: \(r=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\).
Calculate discriminant: \(b^2 - 4ac = 1^2 - 4\times5\times5 = 1 - 100 = -99\).
Substitute into formula: \(r=\frac{-1\pm\sqrt{-99}}{2\times5}=\frac{-1\pm3i\sqrt{11}}{10}\).

Answer:

\(r = \frac{-1 + 3i\sqrt{11}}{10}\) or \(r = \frac{-1 - 3i\sqrt{11}}{10}\)