Chapter 4, Problem 53SGR

(a)

To determine

To find: The value of discriminant.

Answer to Problem 53SGR

The value of discriminant is $D=153$ .

Explanation of Solution

Given information:

The given equation is $2x^2+3x-18=0$ .

Calculation:

Consider the equation $2x^2+3x-18=0$ .

Compare above expression with standard form $a{x}^2+bx+c$ .

Where,

  $a=2$ , $b=3$ , $c=-18$ .

Consider following expression for discriminant.

  $D=b^2-4ac$ ... (1)

Substitute the values in the equation (1)

  $\begin{array}{c}D=b^2-4ac\\ ={\left(3\right)}^2-4\left(2\right)\left(-18\right)\\ =9+144\\ =153\end{array}$

Therefore, the value of discriminant is $D=153$ .

(b)

To determine

To find: The number type of roots.

Answer to Problem 53SGR

The number of roots is $2$ which is real and irrational.

Explanation of Solution

Given information:

The given equation is $2x^2+3x-18=0$

Calculation:

Calculate the number of type roots.

The expression is $x=\frac{-b\pm \sqrt{D}}{2a}$ .

Substitute the value of $D$ in the expression.

  $\begin{array}{c}x=\frac{-3\pm \sqrt{153}}{2a}\\ =\frac{-3\pm \sqrt{153}}{2\left(2\right)}\end{array}$

Therefore, the number of roots is $2$ which is real and irrational.

(c)

To determine

To find: The exact solution of quadratic formula.

Answer to Problem 53SGR

The exact value of quadratic equation is $x=\frac{-3\pm \sqrt{153}}{2\left(2\right)}$ .

Explanation of Solution

Given information:

The given equation is $2x^2+3x-18=0$ .

Calculation:

Substitute the value of $D$

  $\begin{array}{c}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ =\frac{-3\pm \sqrt{153}}{2\left(2\right)}\end{array}$

Therefore the exact value of quadratic equation is $x=\frac{-3\pm \sqrt{153}}{2\left(2\right)}$ .