Chapter 12, Problem 7CR

To determine

To define: The correct option of the expression $2x^2-3x-2=0$ ,solve discriminant of quadratic equation and the options are,

  $\begin{array}{l}\text{a}.\left\{-25\right\}\\ \text{b}\text{.}\left\{25\right\}\\ \text{c}.\left\{-5\right\}\\ \text{d}\text{.}\text{}\left\{5\right\}\end{array}$

Answer to Problem 7CR

The correct option of expression $2x^2-3x-2=0$ is $\text{b}\text{.}\text{25}$ .

Explanation of Solution

Given information:

The expression $2x^2-3x-2=0$ and provided options are,

  $\begin{array}{l}\text{a}.\left\{-25\right\}\\ \text{b}\text{.}\left\{25\right\}\\ \text{c}.\left\{-5\right\}\\ \text{d}\text{.}\text{}\left\{5\right\}\end{array}$

The provided expression is $2x^2-3x-2=0$

The value of $b^2-4ac$ is called the discriminant of the quadratic equation.

The values of $a=2,b=-3\text{and}c=-2$ put into the discriminant of the quadratic equation,

  $\begin{array}{l}{b}^2-4ac\\ ={\left(-3\right)}^2-4\cdot 2\cdot \left(-2\right)\\ =9+16\end{array}$

Furthermore,

  $\begin{array}{l}=9+16\\ =25\end{array}$

So, the discriminant of the quadratic equation is 25.

Thus, the option $b$ is correct.