Chapter 8.1, Problem 1MRE

To determine

To solve the equation over real numbers.

Answer to Problem 1MRE

The solution of the equation is $\frac{5\pm \sqrt{13}}{6}$ .

Explanation of Solution

Given information:

The given equation is:

  $3x^2-5x+1=0$

Formula used:

The following formula is used:

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Calculation :

The solution can be obtained by:

  $\begin{array}{l}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-\left(-5\right)\pm \sqrt{{\left(-5\right)}^2-4\left(3\right)\left(1\right)}}{2\left(3\right)}\\ x=\frac{5\pm \sqrt{25-12}}{6}\\ x=\frac{5\pm \sqrt{13}}{6}\end{array}$

Hence, the solution of the equation is $\frac{5\pm \sqrt{13}}{6}$ .