Chapter 4, Problem 21PT

(a)

To determine

To find: The value of discriminant.

Answer to Problem 21PT

The value of discriminant is $-15$ .

Explanation of Solution

Given information:

The given equation is $2x^2+5x-8=-13$ .

Calculation:

The value of discriminant $b^2-4ac$ is calculated below.

  $\begin{array}{c}{b}^2-4ac=5^2-4\left(2\right)\left(5\right)\\ =-15>0\end{array}$

Therefore, the value of discriminant is $-15$ .

(b)

To determine

To find: The number type of roots.

Answer to Problem 21PT

The two roots are complex roots.

Explanation of Solution

Given information:

the given information $2x^2+5x-8=-13$ .

Calculation:

The discriminant obtained in part $a$ .is negative and thus the two roots are complex roots.

Therefore, the two roots are complex roots.

(c)

To determine

To find: The exact solution of quadratic equation.

Answer to Problem 21PT

The exact value of quadratic equation is $x=\frac{-5\pm i\sqrt{15}}{5}$

Explanation of Solution

Given information:

The given information is $5x^2=-6x+1$ .

Calculation:

The exact solution is found below by using $a=2$ , $b=5$ , $c=5$ and the quadratic formula. $\begin{array}{c}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ =\frac{-5\pm \sqrt{{\left(5\right)}^2-4\left(2\right)\left(5\right)}}{2\left(2\right)}\\ =\frac{-5\pm \sqrt{\left(1\right)15}}{5}\end{array}$

Therefore The exact value roots are $x=\frac{-5\pm i\sqrt{15}}{5}$ .