Chapter 8.5, Problem 7MRE

To determine

To find: whether the roots of the equation are rational, irrational, or imaginary

Answer to Problem 7MRE

The root of the equation is imaginary.

Explanation of Solution

Given information:

The equation is:

  $2x^2-3x+2=0$

Concept used:

The formula of the discriminant is:

  $D=b^2-4ac$ for the equation $a{x}^2+bx+c=0$

If, $D=0$ , then there is irrational root of the equation.

If, $D>0$ , then there is rational root of the equation.

If, $D<0$ , then the roots are imaginary.

Calculation :

The root of the equation can be obtained as:

  $2x^2-3x+2=0$

Now, $a=2,b=-3,c=2$

  $\begin{array}{l}D=b^2-4ac\\ $ D={(-3)}^2-4(2)(2)$ D=9-16\\ D=-5\end{array}$

Since, $D<0$ , so, the roots are imaginary.