Solve this quadratic equation. x² + 5x + 3 = 0

Solution:

The given quadratic equation can be solved by using the formula which provides the roots of the equation:

\(\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\)

The above formula is used for solving the quadratic equation of the form ax² + bx + c

In the given problem:

a = 1; b = 5 and c = 3

Therefore the roots are

\(\frac{-5\pm \sqrt{5^{2}-4(1)(3)}}{2(1)}\)

\(\frac{-5\pm \sqrt{25-12}}{2}\) \(\frac{-5\pm \sqrt{13}}{2}\)

\(\frac{-5}{2} - \frac{\sqrt{13}}{2}\) and \(\frac{-5}{2} + \frac{\sqrt{13}}{2}\)

Solve this quadratic equation. x² + 5x + 3 = 0

Summary:

On solving the quadratic equation. x² + 5x + 3 = 0 we get the following roots \(\frac{-5}{2} - \frac{\sqrt{13}}{2}\) and \(\frac{-5}{2} + \frac{\sqrt{13}}{2}\)