Chapter 1, Problem 23T

Solution

Solve the equation $2x^2-x+6=0$ by quadratic formula.

The solution for the quadratic equation is $x=\left\{\frac{1+i\sqrt{47}}{4},\frac{1-i\sqrt{47}}{4}\right\}$ .

Given:

The quadratic equation is $2x^2-x+6=0$ .

Concept used:

Any quadratic equation of the form $a{x}^2+bx+c=0\text{ where }a\ne 0$ has the solutions $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\mathrm{......}\left(1\right)$

Calculation:

The solution of the quadratic equation $2x^2-x+6=0$ is evaluated with the help of quadratic formula $\left(1\right)$ .

  $\begin{array}{c}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\mathrm{......}\left(\text{From }\left(1\right)\right)\\ =\frac{-\left(-1\right)\pm \sqrt{{\left(-1\right)}^2-4\left(2\right)\left(6\right)}}{2\left(2\right)}\mathrm{......}\left(\because 2x^2-x+6=0\right)\\ =\frac{1\pm i\sqrt{47}}{4}\\ =\left\{\frac{1+i\sqrt{47}}{4},\frac{1-i\sqrt{47}}{4}\right\}\end{array}$

Hence the solution for the quadratic equation is $x=\left\{\frac{1+i\sqrt{47}}{4},\frac{1-i\sqrt{47}}{4}\right\}$ .