Chapter 9.7, Problem 34MR

To determine

To solve the equation using quadratic formula.

Answer to Problem 34MR

The roots are $2.54$ , $0.13$ .

Explanation of Solution

Given equation:

  $3x^2-8x=-1$

Concept used:

The roots of the quadratic equation $a{x}^2+bx+c=0$ , $a\ne 0$ are given by the quadratic formula,

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Calculation:

  $\begin{array}{c}3x^2-8x=-1\\ 3x^2-8x+1=0\end{array}$

By quadratic formula,

  $\begin{array}{c}x=\frac{8\pm \sqrt{{\left(-8\right)}^2-4\left(3\right)\left(1\right)}}{2\left(3\right)}\\ =\frac{8\pm \sqrt{64-12}}{6}\\ =\frac{8\pm \sqrt{52}}{6}\\ =\frac{8\pm 2\sqrt{13}}{6}\end{array}$

Thus,

  $\begin{array}{c}x=\frac{4+\sqrt{13}}{3},\frac{4-\sqrt{13}}{3}\\ =2.54,0.13\end{array}$

Hence, the roots are $2.54$ , $0.13$ .